Test: Refraction & Dispersion By Prism - JEE MCQ

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
 

Dispersive power depends on the material of the prism. When light transitions from one medium to another it bends on the basis of the refractive indices of the two media. Dispersive power is a measure of the amount of difference in the refraction of the highest and lowest wavelengths which enter the prism.

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.

The angle of deviation is minimum when the path of light ray through the prism is symmetrical. i.e., angle of incidence = angle of emergence and path of ray within the prism is parallel to the base of the prism.

The ratio of angular dispersion to the angle of deviation for the mean wavelength is called Dispersive Power. Represented by 

where δ_v − δ_r is the angular dispersion for violet and red lights and δ_r the deviation suffered by the mean light.

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.

is the right answer.

μ=sinisinr

Again for minimum deviation

μ=sin(A+δmin2)sinA2

∴μ=sinisinA2

⇒sinA2=siniμ

⇒sinA2=sin45∘√2=12

⇒A2=30∘

⇒A=60∘

Again i+e=A+δmin

For minimum deviation i=e

∴2i=A+δmin

⇒δmin=2i−A

⇒δmin=2×45∘−60∘=30∘

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.
 

For dispersion without deviation,
(μ₁​−1)×A₁​=(μ₂​−1)×A_2​
μ₁​=1.54, A₁​=4°, μ₂​=1.72
(1.54−1)×4=(1.72−1)×A_2​
⇒ A₂​=3^∘