Test: Refraction through a Prism & Optical Instruments (February 25) - NEET MCQ

Dispersive power of a prism is defined as the ratio between angular dispersion to mean deviation produced by the prism.
If dμ denotes the difference between the refractive indices of material of prism for violet and red light,
ω = δμ / μ – 1
Here ‘μ’ is the refractive index of prism for a mean colour. A mean colour is that colour whose wavelength lies in between that of violet and red. For white light, yellow colour is, generally, taken to be the mean colour.
Since μv is always greater than μr, the dispersive power of a prism is always positive. It depends upon the type of glass used. It is different for crown glass and for flint glass.
 

The resolving power of a telescope is given by RP∝2μsinθ​/122λ
Further, sinθ ∝ tanθ ∝ diameter of the objective.
So, the resolving power of a telescope depends on the diameter of the objective lens.

Infrared: Night vision goggles pick up the infrared light emitted by our skin and objects with heat. In space, infrared light helps us map the dust between stars.
Visible: Our eyes detect visible light. Fireflies, light bulbs, and stars all emit visible light.

Ultraviolet: Ultraviolet radiation is emitted by the Sun and are the reason skin tans and burns. "Hot" objects in space emit UV radiation as well.

X-ray: A dentist uses X-rays to image your teeth, and airport security uses them to see through your bag. Hot gases in the Universe also emit X-rays.

Gamma ray: Doctors use gamma-ray imaging to see inside your body. The biggest gamma-ray generator of all is the Universe.

'u' should be the least distance of distinct vision.
U=-25cm
V=-50
(1/f)=(1/v)-(1/u)
=(-1/50) + (1/25)
=1/50
F=50cm
Hence a convex lens of focal length 50cm should be used.
 

Area of magnification, 
A₁​A₂=μ²
A₁/6​​=100
A_1​=600 cm²

The final image of the moon should be formed at a distance of 100 cm. Using a concave lens of focal length 100 cm will enable him  to see the moon distinctly.

Focal length of lens =-100 cm

The dispersion is the difference in refracting of lights with highest and lowest velocities. Dispersion depends upon the refractive indexes of the two mediums. Thus, depending on the material of the prism.

As per the given condition,
Real depth of the liquid= 1 m
Apparent depth of the liquid =1−0.1=0.9 m
Refractive index of the liquid = Real Depth/Apparent Depth ​=1/0.9​=1.11