Ray Optics and Optical Test

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Ray Optics and Optical Test - 54

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Weekly Quiz Competition

Question 1
1 / -0

The focal length of objective and eye lens of a microscope are $$4\ cm$$ and $$8\ cm$$ respectively. If the least distance of distinct vision is $$24\ cm$$ and object distance is $$4.5\ cm$$ from the objective lens, then the magnifying power of the microscope will be

A
$$18$$

B
$$32$$

C
$$64$$

D
$$20$$

Solution

For objective lens $$\dfrac{1}{f_0}=\dfrac{1}{v_0}-\dfrac{1}{u_0}$$
$$\Rightarrow \dfrac{1}{(+4)}=\dfrac {1}{v_0}-\dfrac{1}{(-4.5)}\Rightarrow v_0=36\ cm$$
$$\therefore | m_D| =\dfrac {v_0}{u_0}\left( 1+\dfrac{D}{f_e}\right) =\dfrac{36}{4.5}\left( 1+\dfrac{24}{8}\right) =32$$
Question 2
1 / -0

One side of a glass slab is silvered as shown. A ray of light is incident on the order side at the angle of incidence $$i = {45^0}$$. Refractive index of glass is given as 1.5. The deviation of the ray of light from its initial path when it comes out of the slab is

A
$${90^0}$$

B
$${180^0}$$

C
$${120^0}$$

D
$${45^0}$$

Solution

From the figure it is clear that the angle between incident ray and the emergent ray is $$90^o$$.
Question 3
1 / -0

If two mirrors are inclined at some angle $$\theta$$. An object is placed between the mirrors and there are 5 images formed for an object, then $$\theta$$ is may be

A
$$45^o$$

B
$$53^o$$

C
$$63^o$$

D
$$75^o$$

Solution

The number of images formed by two mirrors at an angle $$\theta $$ is
$$\begin{array}{l} n=\dfrac { { 360 } }{ \theta } -1 \\ \because n=5\, \, \left( { given } \right) \\ \therefore 5=\dfrac { { 360 } }{ \theta } -1 \\ \therefore \theta =\dfrac { { 360 } }{ 6 } ={ 60^{ 0 } } \end{array}$$
Hence, the angle may be $$63^0$$.
Question 4
1 / -0

A plane mirror produces a magnification of

A
$$-1$$

B
$$+1$$

C
Zero

D
infinity

Solution

The magnification produced by a plane mirror is $$+1$$ implies that the image formed by a plane mirror is virtual$$,$$
erect and of the same size$$,$$ as that of object$$.$$
Hence,
option $$(B)$$ is correct answer.
Question 5
1 / -0

Light of frequency $$5\times 10^{14}\ Hz$$ is travelling in a medium of refractive index $$1.5$$. What is its wavelength ? $$(c=3\times 10^{8}\ ms^{-1})$$

A
$$9000\ \mathring { A } $$

B
$$6000\ \mathring { A } $$

C
$$4500\ \mathring { A } $$

D
$$4000\ \mathring { A } $$

Solution
Question 6
1 / -0

Three glass prisms A, B and C of same refractive indices are placed in contact with each other as shown in fig. 13.77 with no air gap between the prisms. A monochromatic ray of light OP passes through the prism assemble and emerges as QR. The condition of minimum deviation are satisfied in the prisms:

A
A and C

B
B and C

C
A and B

D
in all prisms A,B and C

Solution

In both $$A$$ and $$B$$, the refracted ray is parallel to the base of prism.
Question 7
1 / -0

Three glass prisms A, B and C of same refractive are placed in contact with each other as shown on Fig. 13.77 with no air gap between the prisms. A monochromatic ray of light OP passes through the prism assembly and emerges as QR. The conditions of minimum deviation are satisfied in the prisms:

A
A and C

B
B and C

C
A and B

D
in all prisms A , B and C

Solution

The condition for minimum deviation in a prism is given as
1. $$i = e$$ where $$i$$ is the angle of incidence and $$e$$ is the angle of emergence.
2. $${r_1} = {r_2}$$ where $${r_1}$$ and $${r_2}$$ are the angle of refraction of the two refracting surfaces of the prism.
Hence the first refracted ray inside the prism should be parallel to the base of the prism.
In the figure we can see that the above condition is satisfied by the prisms $$A$$ and $$B$$.

Hence the correct answer is option (C).
Question 8
1 / -0

A fish is a little away below the surface of a table. If the critical angle is $$49^o$$, then the fish could see things above the water surface within an angular angle of

A
$$\theta = 49^o$$

B
$$\theta = 90^o$$

C
$$\theta = 98^o$$

D
$$\theta = 24.5^o$$

Solution

Critical angle = Angle that the light ray in one side will make with the water surface

This angle will be equal to half the range in which the fish can see

$$\implies$$ Angle range $$= 2 \times$$ Critical angle

$$= 2 \times 49=98^0$$

Hence The angular range in which the fish can see above water surface will be $$98^0$$
Question 9
1 / -0

A convex lens forms a real image of a point object placed on its principle axis.If the upper half of the lens is painted black,the image will-

A
be shifted downwards

B
be shifted upwards

C
not be shifted

D
shift on the principal axis

Solution

Converging a portion of lens does not effect position and size of image.
Question 10
1 / -0

When a glass rod is immersed in a liquid of same refractive index, it will _____.

A
Appear bent

B
Disappear

C
Appear longer

D
Not be affected

Solution