Ray Optics and Optical Instruments Test

Result

Ray Optics and Optical Instruments Test - 7

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Weekly Quiz Competition

Question 1
4 / -1

A giant telescope in an observatory has an objective of focal length 19 m and an eye-piece of focal length 1.0 cm. In normal adjustment, the telescope is used to view the moon. What is the diameter of the image of the moon formed by the objective ? The diameter of the moon is 3.5 × 10⁶ m and the radius of the lunar orbit round the earth is 3.8 × 10⁸ m.

A
10 cm

B
12.5 cm

C
15 cm

D
17.5 cm

Solution

As u ≫ f₀ , v = f₀ = 19 m.
Now u = -3.8 × 10⁸ m. Therefore, magnification produced by the objective is

∴ Diameter of the image of moon is 3.5 × 10⁶ × 0.5 × 10^-7 = 0.175 m = 17.5 cm
Question 2
4 / -1

A ray of light travelling in the direction is incident on a plane mirror. After reflection, it travels along the direction The angle of incidence is

A
30^∘

B
45^∘

C
60^∘

D
75^∘

Solution

Let θ be angle between the given rays.

Angle of incidence,
Question 3
4 / -1

The number of capital letters such as A, B, C, D ..... which are not laterally inverted by a plane mirror?

A
6

B
7

C
11

D
13

Solution

The number of capital letters which are not laterally inverted by a plane mirror are A, H, I, M, O, T, U, V, W, X, Y.
∴ Total = 11
Question 4
4 / -1

Two mirrors at an angle θ^∘ produce 5 images of a point. The number of images produced when θ is decreased to θ − 30^∘ is

A
9

B
10

C
11

D
12

Solution

Number of images = , where θ is in degrees

New angle, θ' = θ - 30^∘ = 60^∘ - 30^∘ = 30^∘
Number of images =
Question 5
4 / -1

A man stands symmetrically between two large plane mirrors fixed to two adjacent walls of a rectangular room. The number of images formed are

A
4

B
3

C
2

D
6

Solution

Here, the walls will act as two plane mirrors inclined'to each other at 90^∘(i.e. θ = 90^∘).
The number of images formed is
Question 6
4 / -1

Two plane mirrors M₁ and M₂ are inclined at angle θ as shown in the figure. A ray of light 1, which is parallel to M₁ strikes M₂ and after two reflections, the ray 2 becomes parallel to M₂. The angle θ is

A
0^∘

B
30^∘

C
45^∘

D
60^∘

Solution

Different angles are as shown in figure.

In triangle ABC, θ + θ + θ = 180^∘, θ = 60^∘
Question 7
4 / -1

Two plane mirrors are placed parallel to each other at a distance L apart. A point object O placed between them, at a distance L/3 from obe mirror. Both mirros form multiple image. The distance between any two images cannot be

A
3L/2

B
2L/3

C
2L

D
L
Question 8
4 / -1

Four identical mirrors are made to stand vertically to form a square arrangement as shown in a top view. A ray starts from the midpoint M of mirror AD and after two reflections reaches corner D. Then, angle θ must be

A
tan⁻¹(0.75)

B
cot⁻¹(0.75)

C
sin⁻¹(0.75)

D
cos⁻¹(0.75)

Solution

The ray starting from point M at an angle θ reaches the corner D at the right along a parallel path. Let a be the length of the side.

From figure,

From (i) and (ii), we get

From (ii) and (iii), we get

⇒ 3xy = 2ay (Using (iv))
x = 2a/3
Substituting this value of x in equation (i), we get

or θ = cot⁻¹(0.75)
Question 9
4 / -1

Light incident normally on a plane mirror attached to a galvanometer coil reflects backward as shown in figure. A current in the coil produces a deflection of 3.5^∘ of the mirror. The displacement of the reflected spot of light on a screen placed 1.0 m away is

A
27.5 m

B
48.9 m

C
24.5 m

D
12.2 m

Solution

Angle of deflection is θ = 3.5^∘, Distance, between the screen and the mirror is = 2.0m
The reflected rays get deflected by an amount twice the angle of deflection, i.e., 2θ = 7.0^∘ ∴ tan 2θ = d/2
⇒ d = 2 × tan 7^∘
= 2 × 0.1227
= 0.245m
= 24.5cm
Question 10
4 / -1

A plane mirror is placed along the x-axis facing negative y-axis. The mirror is fixed. A point object is moving with in front of the plane mirror. The relative velocity of image with respect to its object is

A

B

C

D

Solution

Velocity of object,
Velocity of image,
Relative velocity of image with respect to its object