Ray Optics and Optical Instruments

Q1 FREE PREVIEW

PYQ

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of \({f}_{1}\) in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of \({f}_{2}\) when it is immersed in a liquid of refractive index 1.2 . If both the lenses are made of same glass of refractive index 1.5 , the ratio of \({f}_{1}\) and \({f}_{2}\) will be

[JEE Main 2025, 24 Jan (Shift 1)]

a

1:2

b

1:3

c

3:5

d

2:3

✓ Correct answer: b)

1:3

Explanation

Using the lens maker's formula

\(\frac{1}{{f}_{1}}=\left({n}_{\text{glass }}-{n}_{\text{air }}\right)\left(\frac{1}{{R}_{1}}-\frac{1}{{R}_{2}}\right)\)

Since one surface is flat, \({R}_{2}\) is infinity, so

\(\frac{1}{{R}_{2}}=0\)

For the first lens in air (with refractive index 1.5 and radius of curvature 2 cm ):

\(\frac{1}{{f}_{1}}=(1.5-1)\left(\frac{1}{2}\right)\\ {f}_{1}=4cm\)

For the second lens:

\(\frac{1}{{f}_{2}}=\left(\frac{1.5}{1.2}-1\right)\left(\frac{1}{3}-0\right)\\ {f}_{2}=12cm\)

Ratio of focal lengths:

\({f}_{1}:{f}_{2}=4:12=1:3\)

Q2 FREE PREVIEW

PYQ

A point object is placed in air at a distance of 4R on the principal axis of a convex spherical surface of radius of curvature R separating two mediums, air and glass. As the object is moved towards the surface, the image formed is :

a

always real

b

always virtual

c

first virtual and then real

d

first real and then virtual

✓ Correct answer: d)

first real and then virtual

Explanation

To determine the nature of the image formed by a convex spherical surface separating air and glass, we need to consider the refraction of light at the convex surface. The nature of the image (real or virtual) depends on the position of the object relative to the focal point of the convex surface.

Identify the given parameters: object distance (\(u = -4R\)), radius of curvature (\(R\)), and the refractive indices of air (\(n1 = 1\)) and glass (\(n2 > 1\)).

Use the refraction formula for a spherical surface:
\(\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}\)
where \(u\) is the object distance, \(v\) is the image distance, and \(R\) is the radius of curvature.

Substitute the given values into the formula:
\(\frac{n_2}{v} - \frac{1}{-4R} = \frac{n_2 - 1}{R}\)

Solve for the image distance \(v\). As the object moves towards the surface (\(u\) increases from \(-4R\) to \(0\)), analyze how the image distance \(v\) changes. Initially, when the object is far (\(u = -4R\)), the image is virtual. As the object moves closer to the surface, the image becomes real when the object is within the focal length of the convex surface.

Final Answer:
D. first real and then virtual

Q3 FREE PREVIEW

PYQ

A beaker is filled with water (refractive index \(\frac{4}{3}\)) upto a height H . A coin is placed at its bottom. The depth of the coin, when viewed along the near normal direction, will be

a

\(\frac{\mathrm{H}}{4}\)

b

\(\frac{3\mathrm{H}}{4}\)

c

\(H\)

d

\(\frac{4\mathrm{H}}{3}\)

✓ Correct answer: b)

\(\frac{3\mathrm{H}}{4}\)

Explanation

The apparent depth (\({d}_{a}\)) is given by the formula:

\({d}_{a}=\frac{d}{n}\)

where \(d\)is the actual depth of the coin and \(n\) is the refractive index of the medium (water in this case).

\({d}_{a}=\frac{H}{\frac{4}{3}}\)

To solve this, multiply \(H\) by the reciprocal of \(\frac{4}{3}\):

\({d}_{a}=H\times \frac{3}{4}=\frac{3H}{4}\)

Q4 FREE PREVIEW

PYQ

A concave mirror of focal length \(f\) in air is dipped in a liquid of refractive index \(\mu\). Its focal length in the liquid will be:

[JEE Main 2025, 23 Jan (Shift 2)]

a

\(\mu f\)

b

\(\frac{f}{(\mu -1)}\)

c

\(\frac{f}{\mu }\)

d

\(f\)

✓ Correct answer: d)

\(f\)

Explanation

There is no effect of medium on focal length of Spherical mirror.

Q5

PYQ

A beaker is filled with water (refractive index \(\frac{4}{3}\)) upto a height H . A coin is placed at its bottom. The depth of the coin, when viewed along the near normal direction, will be

a

\(\frac{\mathrm{H}}{4}\)

b

\(\frac{3\mathrm{H}}{4}\)

c

\(H\)

d

\(\frac{4\mathrm{H}}{3}\)

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Q6

PYQ

Given a thin convex lens (refractive index \(\mu_2\) ), kept in a liquid (refractive index \({\mu }_{1},{\mu }_{1}<{\mu }_{2}\) ) having radii of curvatures \(\left|{\mathrm{R}}_{1}\right|\) and \(\left|{\mathrm{R}}_{2}\right|\). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

[JEE Main 2025, 23 Jan (Shift 1)]

a

\(\frac{{\mu }_{1}\left|{R}_{1}\right|\cdot {R}_{2}∣}{{\mu }_{2}\left(\left|{R}_{1}\right|+\left|{R}_{2}\right|\right)-{\mu }_{1}\left|{R}_{2}\right|}\)

b

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|\cdot \left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\left|{\mathrm{R}}_{1}\right|}\)

c

\(\frac{\left({\mu }_{2}+{\mu }_{1}\right)\left|{\mathrm{R}}_{1}\right|}{\left({\mu }_{2}-{\mu }_{1}\right)}\)

d

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|\cdot \left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(2\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\sqrt{\left|{\mathrm{R}}_{1}\right|\cdot \left|{\mathrm{R}}_{2}\right|}}\)

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Q7

PYQ

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm , the magnification obtained by the microscope for most suitable viewing by relaxed eye is :

a

250

b

200

c

150

d

125

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Q8

PYQ

A spherical surface of radius of curvature \(R\), separates air from glass (refractive index \(=1.5\) ). The centre of curvature is in the glass medium. A point object ' O ' placed in air on the optic axis of the surface, so that its real image is formed at ' I ' inside glass. The line OI intersects the spherical surface at P and \(\mathrm{PO}=\mathrm{PI}\). The distance PO equals to

[JEE Main 2025, 23 Jan (Shift 1)]

a

3 R

b

1.5 R

c

2 R

d

5 R

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Q9

PYQ

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5D? ['D' stands for dioptre]

[JEE Main 2025, 24 Jan (Shift 1)]

a

0.1

b

0.04

c

0.01

d

0.40

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Q10

PYQ

A concave mirror of focal length \(f\) in air is dipped in a liquid of refractive index \(\mu\). Its focal length in the liquid will be:

[JEE Main 2025, 23 Jan (Shift 2)]

a

\(\mu f\)

b

\(\frac{f}{(\mu -1)}\)

c

\(\frac{f}{\mu }\)

d

\(f\)

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Q11

PYQ

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of \({f}_{1}\) in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of \({f}_{2}\) when it is immersed in a liquid of refractive index 1.2 . If both the lenses are made of same glass of refractive index 1.5 , the ratio of \({f}_{1}\) and \({f}_{2}\) will be

a

1:2

b

1:3

c

3:5

d

2:3

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Q12

PYQ

The speed of light in two media ' 1 ' and ' 2 ' are \({v}_{1}\) and \({v}_{2}\left(>{v}_{1}\right)\) respectively. For a ray of light to undergo total internal reflection at the interface of these two media, it must be incident from

a

medium ' 1 ' and at an angle greater than \({\sin }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

b

medium ' 1 ' and at an angle greater than \({\cos }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

c

medium ' 2 ' and at an angle greater than \({\sin }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

d

medium ' 2 ' and at an angle greater than \({\cos }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

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Q13

PYQ

Given a convex lens of refractive index \({\mu }_{2}\) in a liquid of refractive index \({\mu }_{1},{\mu }_{1}<{\mu }_{2}\) having radii of curvature \({\mathrm{R}}_{1},{\mathrm{R}}_{2}\mathrm{and}{\mathrm{R}}_{2}\) surface is silver polished. Where should an object be placed on the optical axis so that the real and inverted image is formed at the same place.

(Shift - I Memory Based)

a

\(\frac{\left({\mu }_{2}+{\mu }_{1}\right)\left|{\mathrm{R}}_{1}\right|}{\left({\mu }_{2}-{\mu }_{1}\right)}\)

b

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|.\left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\left|{\mathrm{R}}_{2}\right|}\)

c

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|.\left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(2\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\sqrt{\left|{\mathrm{R}}_{1}\right|\left|{\mathrm{R}}_{2}\right|}}\)

d

\(\frac{{\mu }_{1}\left|{\mathrm{R}}_{1}\right|.\left|{\mathrm{R}}_{2}\right|}{{\mu }_{2}\left(\left|{\mathrm{R}}_{1}\right|+\left|{\mathrm{R}}_{2}\right|\right)-{\mu }_{1}\left|{\mathrm{R}}_{1}\right|}\)

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Q14

PYQ

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm , the magnification obtained by the microscope for most suitable viewing by relaxed eye is :

a

250

b

200

c

150

d

125

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Q15

PYQ

The optical power of a lens is increased from \(0.1\text{ }\text{D}\) to \(2.5\text{ }\text{D}\). What is the relative shift in the focal length of the lens?

(Shift I Memory Based)

a

24/25

b

13/10

c

21/25

d

11/10

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Q16

PYQ

For a concave mirror, the distance between the object and image is 20 cm , and the magnification is -3 . Find the focal length of the mirror.

(Shift - II Memory Based)

a

5 cm

b

7.5 cm

c

10 cm

d

15 cm

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Q17

PYQ

The speed of light in two media ' 1 ' and ' 2 ' are \({v}_{1}\) and \({v}_{2}\left(>{v}_{1}\right)\) respectively. For a ray of light to undergo total internal reflection at the interface of these two media, it must be incident from

a

medium ' 1 ' and at an angle greater than \({\sin }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

b

medium ' 1 ' and at an angle greater than \({\cos }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

c

medium ' 2 ' and at an angle greater than \({\sin }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

d

medium ' 2 ' and at an angle greater than \({\cos }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

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Q18

PYQ

The speed of light in two media ' 1 ' and ' 2 ' are \({v}_{1}\) and \({v}_{2}\left(>{v}_{1}\right)\) respectively. For a ray of light to undergo total internal reflection at the interface of these two media, it must be incident from

a

medium ' 1 ' and at an angle greater than \({\sin }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

b

medium ' 1 ' and at an angle greater than \({\cos }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

c

medium ' 2 ' and at an angle greater than \({\sin }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

d

medium ' 2 ' and at an angle greater than \({\cos }^{-1}\left(\frac{{v}_{1}}{{v}_{2}}\right)\)

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Q19

PYQ

A spherical surface of radius of curvature \(R\), separates air from glass (refractive index \(=1.5\) ). The centre of curvature is in the glass medium. A point object ' O ' placed in air on the optic axis of the surface, so that its real image is formed at ' I ' inside glass. The line OI intersects the spherical surface at P and \(\mathrm{PO}=\mathrm{PI}\). The distance PO equals to

[JEE Main 2025, 23 Jan (Shift 1)]

a

3 R

b

1.5 R

c

2 R

d

5 R

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Q20

PYQ

A beaker is filled with water (refractive index \(\frac{4}{3}\)) upto a height H . A coin is placed at its bottom. The depth of the coin, when viewed along the near normal direction, will be

a

\(\frac{\mathrm{H}}{4}\)

b

\(\frac{3\mathrm{H}}{4}\)

c

\(H\)

d

\(\frac{4\mathrm{H}}{3}\)

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Q21

PYQ

The refractive index of a prism with apex angle A is \(\cot \frac{A}{2}\). The angle of minimum deviation is :

[JEE Main 2024, 31 Jan (Shift 1)]

a

\({\delta }_{m}=180^\circ -A\)

b

\({\delta }_{m}=180^\circ -3A\)

c

\({\delta }_{m}=180^\circ -4A\)

d

\({\delta }_{m}=180^\circ -2A\)

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Q22

PYQ

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' \(h\) ' in terms of the angle of incidence ' \(i\) ' and angle of refraction ' \(r\) ', if the glass slab is placed in air medium?

[JEE Main 2025, 23 Jan (Shift 1)]

a

\(\frac{h\cos (i-r)}{\sin r}\)

b

\(h\)

c

\(\frac{\mathrm{htan}(\mathrm{i}-\mathrm{r})}{\mathrm{tanr}}\)

d

\(\frac{h\sin (i-r)}{\cos r}\)

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Q23

PYQ

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1 D from 2.5D? ['D' stands for dioptre]

[JEE Main 2025, 24 Jan (Shift 1)]

a

0.1

b

0.04

c

0.01

d

0.40

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Q24

PYQ

A beaker is filled with water (refractive index \(\frac{4}{3}\)) upto a height H . A coin is placed at its bottom. The depth of the coin, when viewed along the near normal direction, will be

a

\(\frac{\mathrm{H}}{4}\)

b

\(\frac{3\mathrm{H}}{4}\)

c

\(H\)

d

\(\frac{4\mathrm{H}}{3}\)

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Q25

PYQ

A convex refracting surface curved towards medium A separates two media A and B, where medium A has a refractive index of 1.3 and medium B has a refractive index of 1.4. An object is placed 26 cm in medium A along the principal axis. If the image is formed at infinity, find the radius of curvature of the surface.

(Shift - II Memory Based)

a

2 cm

b

50 cm

c

60 cm

d

70 cm

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Q26

PYQ

A point object is placed in air at a distance of 4R on the principal axis of a convex spherical surface of radius of curvature R separating two mediums, air and glass. As the object is moved towards the surface, the image formed is :

a

always real

b

always virtual

c

first virtual and then real

d

first real and then virtual

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Q27

PYQ

Given is a thin convex lens of glass (refractive index \(\mu\) ) and each side having radius of curvature \(R\). One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?

[JEE Main 2025, 22 Jan (Shift 1)]

a

\(\mu \mathrm{R}\)

b

\(R/(2\mu -1)\)

c

\(R/(2\mu -3)\)

d

\(R/\mu\)

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Q28

PYQ

A point object is placed in air at a distance of 4R on the principal axis of a convex spherical surface of radius of curvature R separating two mediums, air and glass. As the object is moved towards the surface, the image formed is :

a

always real

b

always virtual

c

first virtual and then real

d

first real and then virtual

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Q29

PYQ

A thin prism \({P}_{1}\) with angle 4° made of glass having refractive index 1.54 , is combine with another thin prism \({P}_{2}\) made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism \({P}_{2}\) in degrees is

(Shift - I Memory based)

a

16/3

b

4

c

3

d

1.5

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Q30

PYQ

A plano-convex lens has a radius of curvature of 2 cm and a refractive index of 1.5. Its focal length is \({f}_{1}\) in air and \({f}_{2}\) in a medium with a refractive index of 1.2. Calculate the ratio \(\frac{{f}_{1}}{{f}_{2}}\).

(Shift - I Memory Based)

a

1/2

b

2/3

c

3/4

d

1/3

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Q31

PYQ

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm , the magnification obtained by the microscope for most suitable viewing by relaxed eye is :

a

250

b

200

c

150

d

125

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Q32

PYQ

If angle of prism is equal to the angle of minimum deviation. Given \(\mu =\sqrt{3}\), then find the angle of prism.

(Shift - II Memory Based)

a

\(60^\circ\)

b

\(30^\circ\)

c

\(45^\circ\)

d

\(10^\circ\)

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Q33

PYQ

At the interface between two materials having refractive indices \({n}_{1}\) and \({n}_{2}\), the critical angle for reflection of an em wave is \({\theta }_{1C}\). The \({n}_{2}\) material is replaced by another material having refractive index \({n}_{3}\) such that the critical angle at the interface between \({n}_{1}\) and \({n}_{3}\) materials is \({\theta }_{2C}\). If \({n}_{3}>{n}_{2}>{n}_{1};\frac{{n}_{2}}{{n}_{3}}=\frac{2}{5}\) and \(\sin {\theta }_{2C}-\sin {\theta }_{1C}=\frac{–1}{2}\), then \({\theta }_{1C}\) is

[JEE Main 2025, 29 Jan (Shift 1)]

a

\({\sin }^{-1}\left(\frac{2}{3}\right)\)

b

\({\sin }^{-1}\left(\frac{1}{6{n}_{1}}\right)\)

c

\({\sin }^{-1}\left(\frac{5}{6}\right)\)

d

\({\sin }^{-1}\left(\frac{1}{3{n}_{1}}\right)\)

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Q34

PYQ

Assertion (A) : Plane and convex mirrors cannot produce real images under any circumstance.

Reason (R) : A virtual image cannot serve as an object to produce a real image.

a

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

b

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

c

Assertion (A) is true, but Reason (R) is false.

d

Assertion (A) is false and Reason (R) is also false.

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Q35

PYQ

Assertion (A) and Reason (R) type questions. Two statements are given — one labelled Assertion (A) and the other labelled Reason (R).
Select the correct answer from the codes (A), (B), (C) and (D)as given below.

Assertion (A) : Although the surfaces of a goggle lens are curved, it does not have any power.

Reason (R) : In case of goggles, both the curved surfaces are curved on the same side and have equal radii of curvature.

a

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

b

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

c

Assertion (A) is true, but Reason (R) is false.

d

Both Assertion (A) and Reason (R) are false.

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Q36

PYQ

Two statements are given - one labelled Assertion (A) and the other labelled Reason \((R)\). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A) : Plane and convex mirrors cannot produce real images under any circumstance.

Reason ( \(R\) ): A virtual image cannot serve as an object to produce a real image.

a

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

b

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

c

Assertion (A) is true, but Reason (R) is false.

d

Assertion (A) is false and Reason (R) is also false.

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Q37

PYQ

Two statements are given - one labelled Assertion (A) and the other labelled Reason \((R)\). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A) : A convex lens, when immersed in a liquid, disappears.

Reason ( \(R\) ): The refractive indices of material of the lens and the liquid are equal.

a

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

b

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

c

Assertion (A) is true, but Reason (R) is false.

d

Assertion (A) is false and Reason (R) is also false.

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Q38

PYQ

Assertion (A) and Reason (R) type questions. Two statements are given one labelled Assertion (A) and the other labelled Reason
(R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.

Assertion (A) : The magnifying power of a compound microscope is negative.

Reason (R) : The final image formed is erect with respect to the object.

a

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

b

Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

c

Assertion (A) is true, but Reason (R) is false.

d

Assertion (A) is false and Reason (R) is also false.

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Q39

PYQ

A ray of monochromatic light propagating in air, is incident on the surface of water. Which of the following will be the same for the reflected and refracted rays?

a

Energy carried

b

Speed

c

Frequency

d

Wavelength

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Q40

PYQ

The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm. The refractive index of the lens material is:

a

\(1.2\)

b

\(1.4\)

c

\(1.5\)

d

\(1.8\)

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Q41

PYQ

The magnifying power of a telescope with tube length \( 60 \mathrm{~cm} \) is 5 . What is the focal length of its eye piece ?

a

\( 30 \mathrm{~cm} \)

b

\( 10 \mathrm{~cm} \)

c

\( 40 \mathrm{~cm} \)

d

\( 20 \mathrm{~cm} \)

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