Geometrical Optics Questions — JEE Physics

Q1

The magnifying power of a telescope with tube 60 cm is 5. What is the focal length of its eye piece ?

A 40 cm

B 10 cm

C 30 cm

D 20 cm

Correct Answer

Option B

Solution

For telescope Tube length (L) = f0 + fe and magnification (m) =

{{{f_0}} \over {{f_e}}}

= 5 where fo and fe are focal length of objective and eyepiece. $\therefore$ f0 + fe = 60 $\therefore$ fo = 50 cm fe = 10 cm

Q2

A vessel of depth 2h is half filled with a liquid of refractive index

2\sqrt 2

and the upper half with another liquid of refractive index

\sqrt 2

. The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :

A

{h \over {\sqrt 2 }}

B

{h \over {3\sqrt 2 }}

C

{3 \over 4}h\sqrt 2

D

{h \over {2\left( {\sqrt 2 + 1} \right)}}

Correct Answer

Option C

Solution

D =

{{{t_1}} \over {{\mu _1}}} + {{{t_2}} \over {{\mu _2}}}

=

{h \over {\sqrt 2 }} + {h \over {2\sqrt 2 }}

=

{3 \over 4}h\sqrt 2

Q3

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :- A. Real B. Erect C. Smaller in size then object D. Laterally inverted Choose the most appropriate answer from the options given below :

A B and D only

B A, C, and D only

C A and D only

D B and C only

Correct Answer

Option A

Solution

Plane mirror forms erect, same sized, laterally inverted and virtual image of real object.

Q4

A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances x1 and x2 (x1 > x2) from the lens. The ratio of x1 and x2 is :-

A 3 : 1

B 2 : 1

C 5 : 3

D 4 : 3

Correct Answer

Option A

Solution

Magnification is 2 If image is real,

{x_1} = {{3f} \over 2}

If image is virtual,

{x_2} = {f \over 2}

{{{x_1}} \over {{x_2}}} = 3:1

Q5

Red light differs from blue light as they have :

A Different frequencies and same wavelengths

B Different frequencies and different wavelengths

C Same frequencies and different wavelengths

D Same frequencies and same wavelengths

Correct Answer

Option B

Solution

Red light and blue light have different wavelength and different frequency.

Q6

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is –3, then the magnitude of the radius of curvature of the mirror is :

A 3.75 cm

B 15 cm

C 7.5 cm

D 30 cm

Correct Answer

Option B

Solution

\begin{aligned} & \mathrm{m}=-3=-\frac{\mathrm{v}}{\mathrm{u}} \text{ and } \mathrm{v}-\mathrm{u}=20 \mathrm{~cm} \\ & \mathrm{f}=\frac{\mathrm{vu}}{\mathrm{v}+\mathrm{u}}=\frac{(-30)(-10)}{-30-10} \\ & \therefore \mathrm{R}=+15 \end{aligned}

Q7

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:

A

\mu f

B

f

C

\dfrac{f}{\mu}

D

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

Correct Answer

Option B

Solution

When a concave mirror is dipped in a liquid, its focal length is still determined by the geometry of the mirror.

For a spherical concave mirror, the focal length is given by

f = \frac{R}{2}

where

R

is the radius of curvature of the mirror.

This derivation comes solely from geometrical considerations and the law of reflection, which states that the angle of incidence equals the angle of reflection.

Since reflection is independent of the medium in which the mirror is immersed, the focal length remains unchanged.

Thus, even when the mirror is in a liquid of refractive index $\mu$ , its focal length is still

f.

The correct answer is Option B:

f

.

Q8

The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440

\mathop A\limits^o

is used to see th object will be :

A 8.1

\times

106

B 10.0

\times

107

C 8.2

\times

105

D 1.0

\times

10

-

8

Correct Answer

Option C

Solution

R.P. = {1 \over {1.22\,\lambda /a}}

= {{24.4 \times {{10}^{ - 2}}} \over {1.22 \times 2440 \times {{10}^{ - 10}}}}

= 8.2 \times {10^5}

Q9

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) parallel to the first mirror (M1). The angle between the two mirrors will be :

A 45o

B 60o

C 75o

D 90o

Correct Answer

Option B

Solution

Let the angle between two mirrors are $\theta$ .

We know sum of angles of triangle = 180o $\therefore$ 3 $\theta$ = 180o $\Rightarrow$ $\theta$ = 60o

Q10

An initially parallel cylindrical beam travels in a medium of refractive index

\mu \left( I \right) = {\mu _0} + {\mu _2}\,I,

where

{\mu _0}

and

{\mu _2}

are positive constants and

I

is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. The speed of light in the medium is

A minimum on the axis of the beam

B the same everywhere in the beam

C directly proportional to the intensity

I

D maximum on the axis of the beam

Correct Answer

Option A

Solution

The speed of light

(c)

in a medium of refractive index

\left( \mu \right)

is given by

\mu = {{{c_0}} \over c},

where

{c_0}

is the speed of light in vacuum $\therefore$

c = {{{c_0}} \over \mu } = {{{c_0}} \over {{\mu _0} + {\mu _2}\left( I \right)}}

As

I

is decreasing with increasing radius, it is maximum on the axis of the beam. Therefore,

c

is minimum on the axis of the beam.