Ray Optics Chapter-Wise Test 10

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A ray of light passes from glass (\( n = 1.52 \)) to air at an angle of incidence of \( 45^\circ \). What happens?

Critical angle: \( \sin i_c = \frac{n_2}{n_1} = \frac{1}{1.52} \approx 0.658 \Rightarrow i_c \approx 41.1^\circ \).

Since \( i = 45^\circ > i_c \), total internal reflection occurs.

Refraction at 50°
Refraction at 60°
Total internal reflection
No change
3

A prism of angle \( 60^\circ \) has a refractive index of \( 1.4 \). What is the angle of minimum deviation?

For a thin prism: \( D_m = (n - 1) A \).

\( n = 1.4 \), \( A = 60^\circ \).

\( D_m = (1.4 - 1) \times 60 = 0.4 \times 60 = 24^\circ \).

20°
24°
28°
30°
2

In a concave mirror, under what condition is the image formed virtual and magnified?

For a concave mirror, a virtual and magnified image is formed when the object is placed between the focal point (F) and the pole (P). Here, the reflected rays diverge, and their backward extensions converge behind the mirror, producing a virtual, erect, and magnified image.

Object beyond the center of curvature
Object at the focal point
Object between focal point and pole
Object at the center of curvature
3

In a refracting telescope, why does the objective lens have a larger aperture than the eyepiece?

The objective lens in a refracting telescope has a larger aperture to collect more light from distant objects, enhancing brightness and resolution. The eyepiece, with a smaller aperture, magnifies this image, requiring less light-gathering capacity for viewing.

To invert the image
To reduce chromatic aberration
To decrease magnification
To gather more light for brightness
4

A convex lens (\( f = 30 \, \text{cm} \)) and a concave lens (\( f = 15 \, \text{cm} \)) are in contact. What is the effective focal length?

\( f_1 = 30 \, \text{cm} \), \( f_2 = -15 \, \text{cm} \).

\( \frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{30} + \frac{1}{-15} = \frac{1 - 2}{30} = \frac{-1}{30} \).

\( f = -30 \, \text{cm} \) (diverging system).

-20 cm
-25 cm
-30 cm
-35 cm
3

In a plane mirror, why does the image distance equal the object distance?

In a plane mirror, light reflects such that the angle of incidence equals the angle of reflection. This symmetry ensures that the perpendicular distance from the object to the mirror equals the apparent distance of the image behind it, as the image forms along the normal extended backward.

Due to light converging behind the mirror
Due to the mirror’s curvature
Due to light dispersion
Due to equal angles of incidence and reflection
4

A prism of angle \( 40^\circ \) and refractive index \( 1.5 \) produces what minimum deviation?

For a thin prism: \( D_m = (n - 1) A \).

\( n = 1.5 \), \( A = 40^\circ \).

\( D_m = (1.5 - 1) \times 40 = 0.5 \times 40 = 20^\circ \).

15°
18°
22°
20°
4

An object at a depth of \( 19.95 \, \text{cm} \) in water (\( n = 1.33 \)) is viewed normally. What is the apparent depth?

Apparent depth = \( \frac{\text{real depth}}{n} \).

Real depth = \( 19.95 \, \text{cm} \), \( n = 1.33 \).

Apparent depth = \( \frac{19.95}{1.33} \approx 15 \, \text{cm} \).

15 cm
20 cm
25 cm
10 cm
1

In a plane mirror, what property ensures that the image is not distorted?

The flat surface of a plane mirror ensures that all incident rays reflect with equal angles of incidence and reflection, maintaining the object’s proportions and shape. Curved surfaces would distort the image by altering ray directions unevenly.

Curvature of the mirror
Thickness of the mirror
Refractive index of the glass
Flatness of the reflecting surface
4

What is the primary advantage of using a combination of lenses in optical instruments like microscopes?

A combination of lenses allows for greater magnification and improved image quality. The objective lens forms an initial image, which the eyepiece magnifies further, while multiple lenses can correct aberrations (e.g., chromatic, spherical), enhancing sharpness and clarity.

Reduces the weight of the instrument
Increases magnification and corrects aberrations
Eliminates the need for a light source
Produces a virtual initial image
2

A lens has a power of \( +2.5 \, \text{D} \). What is its focal length in centimeters?

Power: \( P = \frac{1}{f} \) (in meters).

\( P = +2.5 \, \text{D} \Rightarrow 2.5 = \frac{1}{f} \Rightarrow f = \frac{1}{2.5} = 0.4 \, \text{m} = 40 \, \text{cm} \).

30 cm
35 cm
40 cm
45 cm
3

Why does a convex lens produce chromatic aberration when used with white light?

Chromatic aberration occurs in a convex lens because different wavelengths of white light refract by different amounts due to the lens material’s varying refractive index for each wavelength. Shorter wavelengths (e.g., blue) focus closer than longer ones (e.g., red), causing color fringing.

Due to light reflection
Due to uniform refraction
Due to lens thickness
Due to wavelength-dependent refraction
4

Why does a concave mirror used in a reflecting telescope require precise curvature?

The precise curvature of a concave mirror ensures that all parallel rays from a distant object converge accurately to a single focal point. Any deviation in curvature causes spherical aberration, blurring the image and reducing the telescope’s resolving power.

To increase chromatic aberration
To reduce the focal length
To enhance magnification
To ensure rays converge to a single point
4

A simple microscope with a focal length of \( 10 \, \text{cm} \) forms an image at \( 25 \, \text{cm} \). What is the magnification?

Magnification: \( m = 1 + \frac{D}{f} \).

\( D = 25 \, \text{cm} \), \( f = 10 \, \text{cm} \).

\( m = 1 + \frac{25}{10} = 1 + 2.5 = 3.5 \).

2.5
3.5
4.5
5.5
2

An object is at a depth of \( 13.3 \, \text{cm} \) in a medium with refractive index \( 1.33 \). What is the apparent depth?

Apparent depth = \( \frac{\text{real depth}}{n} \).

Real depth = \( 13.3 \, \text{cm} \), \( n = 1.33 \).

Apparent depth = \( \frac{13.3}{1.33} = 10 \, \text{cm} \).

10 cm
12 cm
14 cm
16 cm
1

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