Test: Ray Optics and Optical Instruments - 2 - CUET Humanities MCQ

If length of image is I, then angle subtended by the object at the lens = angle subtended by the image at the lens.
i.e. 1 x 10^-3 = I/f 
I = 50 x 1 x 10^-3
I = 0.5mm

Angular magnification is the ratio of the focal length of the objective to the focal length of the eyepiece.
Therefore, M = F₁/F₂

When light goes from one medium to another, the frequency of light, and phase of light do not change.
However, the velocity of light and wavelength of light change.
So, velocity of light in glass
v_g = 
or v_m - v_g = v_m - 
∴ 6.25 × 10⁷ = v_m
= 2.5 × 10⁸ m/s

Focal length of the objective lens, f_o = 144 cm
Focal length of the eyepiece, f_e = 6.0 cm
The magnifying power of the telescope is given as

The separation between the objective lens and the eyepiece is calculated as:

L = 144 + 6 = 150 cm
Hence, the magnifying power of the telescope is 24, and the separation between the objective lens and the eyepiece is 150 cm.

Angular dispersion,

The water molecules of oceans scatter blue light more strongly as compared to the light of other colours. So, oceans appear bluish in colour.

The refractive index of glass prism is:
 =  = 
, where v is the speed of the light in glass.
v = 

Size of the candle, h = 2.5 cm
Image size = h'
Object distance, u = − 27 cm
Radius of curvature of the concave mirror, R = −36 cm
Focal length of the concave mirror, f = R/2 = -18 cm
Image distance = v
The image distance can be obtained using the mirror formula:

Therefore, the screen should be placed 54 cm away from the mirror to obtain a sharp image.