Ray Optics and Optical Test

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Ray Optics and Optical Test - 47

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Weekly Quiz Competition

Question 1
1 / -0

While finding the refractive index of a glass slab, the travelling microscope is focussed on ink dot on a white paper at position 4.320 cm. When a glass slab is placed on this ink dot on paper, the microscope is raised through 1.80 cm. The thickness of glass slab of refractive index $$\dfrac{3}{2}$$ is :

A
$$\dfrac{1}{0.8}$$ cm

B
2.70 cm

C
5.4 cm

D
1.2 cm

Solution

shift$$=t\left[ 1-\cfrac { 1 }{ \mu } \right] \\ 1.8=t\left[ 1-\cfrac { 1 }{ { 3 }/{ 2 } } \right] \\ 1.8=t\times \cfrac { 1 }{ 3 } \\ \therefore t=5.4cm$$
Question 2
1 / -0

The refractive index of glass with respect to air is $$\dfrac{3}{2}$$ and that of water with respect to air is $$\dfrac{3}{2}$$. What is the refractive index of glass with respect to water?

A
$$9 : 8$$

B
$$1 : 2$$

C
$$2 : 1$$

D
$$8 : 9$$

Solution

Given,

Refractive index of glass=$$\dfrac{3}{2}$$

Refractive index of water=$$\dfrac{4}{3}$$

Refractive Index of glass with respect to water= $$\dfrac{3/2}{4/3}$$
=$$\dfrac{9}{8}$$
Question 3
1 / -0

The phenomenon of bending of light at the surface of separation of two media is called :

A
Refraction of light

B
Reflection of light

C
Deflection of light

D
Absorption of light

Solution

When light travels from one medium to another, the light gets bent and this phenomenon is called refraction of light. The bending of light is due to the different speeds of light in different media.
Question 4
1 / -0

Which of the following forms a virtual and erect image for all positions of the object ?

A
Concave lens

B
Concave mirror

C
Convex mirror

D
Both (a) and (c)

Solution

Concave lens and convex mirror are diverging in nature. They form virtual and erect images.
Question 5
1 / -0

A ray of light is incident on a thick slab of glass of thickness t as shown in the figure. The emergent ray is parallel to the incident ray but displaced sideways by a distance d. If the angles are small then d is

A
$$t\left(1-\dfrac{i}{r}\right)$$

B
$$rt\left(1-\dfrac{i}{r}\right)$$

C
$$it\left(1-\dfrac{r}{i}\right)$$

D
$$t\left(1-\dfrac{r}{i}\right)$$

Solution

The lateral shift occur ed in the ray is given by:
$$d=\dfrac{t sin(i-r)}{cos\ r }$$

For small angle given, $$ sin(i−r)\approx i−r$$
$$cos\ r\approx 1$$

Hence, $$d= t(i-r)= it\bigg(1- \dfrac ri\bigg)$$

So, option $$(C)$$ is correct.
Question 6
1 / -0

There is an insect inside a cabin eying towards a thick glass plate $$P_1$$. Insect sees the images of light source across the glass plate $$P_1$$ outside the cabin. The cabin is made of thick glass plates of refractive index $$ \mu =\frac{3}{2}$$ and thickness is 3 cm. The insect is eying from the middle of the cabin as shown in the figure. ( glass plates are partially reflective and consider only paraxial rays)
At what distance ( from the eye of insect) will the eye see the first image?

A
5 cm

B
7cm

C
11 cm

D
14cm

Solution

$$ \begin{array}{l} \text { The insect can see the light because of the } \\ \text { rays which refract at } P_{2} \text { and which } \\ \text { reflect at } P_{1} \\ \text { Hence we have to consider shift at } P_{2} \\ \text { and mirror at } P_{1} \end{array} $$
$$ \begin{array}{l} \text { Shift of the light ray at } P_{2} \\ \text { Shift }=t\left(1-\dfrac{1}{\mu}\right) \\ \text { where. } \quad \mu=\text { refractive index of slab } \\ t=\text { thick ness of slab. } \\ \text { shift }=3\left(1-\dfrac{1}{\dfrac{3}{2}}\right) \\ =1 \mathrm{~cm} \\ =\text{so distance of refracted object from P_{1}}\\ =3+3+3+2 \end{array} $$

$$=11 \mathrm{~cm}$$
Distance of the first image seen by eye = Image distance form mirror + object distance from mirror
$$\begin{array}{l}=11+3\\=14\mathrm{~cm}\end{array}$$
so option $$D$$ is correct.
Question 7
1 / -0

Of the following instruments, which one would be used for navigating a ship?

A
Telescope

B
Sonometer

C
Aneroid barometer

D
Sextant

Solution
Question 8
1 / -0

Light is incident on a glass surface at polarizing angle of $$57.5^{\circ}$$. Then the angle between the incident ray and the refracted ray is:

A
$$57^{\circ}$$

B
$$115^{\circ}$$

C
$$205^{\circ}$$

D
$$145^{\circ}$$

Solution

Given that,

Polarizing angle for glass = $$57.5^{0}$$

Angle of refraction = $$r$$

Now, refractive index of the glass

$$ \mu =\tan {{\theta }_{p}} $$

$$ 1.4=\tan ({{57.5}^{0}}) $$

Now, from Snell’s law

$$ {{\mu }_{1}}\sin i={{\mu }_{2}}\sin r $$

$$ 1\times \sin \left( {{57.5}^{0}} \right)=1.4\times \sin r $$

$$ \sin r=\frac{0.81419}{1.4} $$

$$ \sin r=0.5816 $$

$$ r={{\sin }^{-1}}\left( 0.5816 \right) $$

$$ r=0.6207 $$

Now, angle of deviation

$$ \delta =i-r $$

$$ \delta =57.5-0.6207 $$

$$ \delta =56.87 $$

$$ \delta ={{57}^{0}} $$

Hence, the angle between the incident ray and the refracted ray is $$57^{0}$$
Question 9
1 / -0

A convergent beam of light passes through a diverging lens of focal length 0.2 m and comes to focus 0.3 m behind the lens. The position of the point at which the beam would converge in the absence of the lens is :

A
0.12 m

B
0.6 m

C
0.3 m

D
0.15 m

Solution

Here, $$f=-0.2m,v=+0.3m$$
from lens equation

$$\dfrac {1 }{ v } -\dfrac { 1}{ u } =\dfrac { 1 }{ f } $$

$$\dfrac { 1 }{ u } =\dfrac { 1 }{ v } -\dfrac { 1 }{f } =\dfrac {1 }{0.3 } -\dfrac { 1 }{0.2 } =\dfrac {25 }{ 3 } $$

$$u=\dfrac { 3}{ 25 } =0.12m$$

Therefore, in the absence of lens, the beam would coverage at a distance of $$0.12m$$ to the right of the concave lens.
Question 10
1 / -0

The minimum distance between an object and its real image formed by a convex lens is:

A
1.5 f

B
2 f

C
2.5 f

D
4 f

Solution

Four times the focal length, we have the formula,
$$\dfrac{1}{u}+\dfrac{1}{v}=\dfrac{1}{f}$$ where,
$$u,v$$ are the object and image distnaces and f is the focal length.
The minimum distnace is achieved when $$u=v=2f$$
Coincidentally the magnification is -1. (The image is same size as the object,but inverted)

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Re-Attempt Weekly Quiz Competition

Ray Optics and Optical Test - 47

Result

Ray Optics and Optical Test - 47

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SHARING IS CARING

Question 1

$$\dfrac{1}{0.8}$$ cm

2.70 cm

5.4 cm

1.2 cm

Solution

Question 2

$$9 : 8$$

$$1 : 2$$

$$2 : 1$$

$$8 : 9$$

Solution

Question 3

Refraction of light

Reflection of light

Deflection of light

Absorption of light

Solution

Question 4

Concave lens

Concave mirror

Convex mirror

Both (a) and (c)

Solution

Question 5

$$t\left(1-\dfrac{i}{r}\right)$$

$$rt\left(1-\dfrac{i}{r}\right)$$

$$it\left(1-\dfrac{r}{i}\right)$$

$$t\left(1-\dfrac{r}{i}\right)$$

Solution

Question 6

5 cm

7cm

11 cm

14cm

Solution

Question 7

Telescope

Sonometer

Aneroid barometer

Sextant

Solution

Question 8

$$57^{\circ}$$

$$115^{\circ}$$

$$205^{\circ}$$

$$145^{\circ}$$

Solution

Question 9

0.12 m

0.6 m

0.3 m

0.15 m

Solution

Question 10

1.5 f

2 f

2.5 f

4 f

Solution

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