This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Ray Optics – Refraction through a Prism”.

1. What is the angle between the incident ray and the emergent ray in a prism called?

a) Angle of deviation

b) Angle of refraction

c) Angle of reflection

d) Angle of dispersion

View Answer

Explanation: A prism is a homogenous, transparent medium enclosed two plane surfaces inclined at an angle. These surfaces are called the refracting surfaces and the angle between the incident ray and emergent ray is known as the angle of deviation.

2. Identify the prism formula from the following.

a) μ=\(\frac {sin [ \frac {A – \delta_m}{2} ] }{ sin(\frac {A}{2}) } \)

b) μ=\(\frac {sin [ \frac {A + \delta_m}{4} ] }{ sin(\frac {A}{2}) } \)

c) μ=\(\frac {sin [ \frac {A + \delta_m}{2} ] }{ sin(\frac {A}{2}) } \)

d) μ=\(\frac {sin [ \frac {A + \delta_m}{2} ] }{ cos(\frac {A}{2}) } \)

View Answer

Explanation: The refractive index of the material of the prism is given as:

μ=\(\frac {sin [ \frac {A + \delta_m}{2} ] }{ sin(\frac {A}{2}) } \)

Where A ➔ Angle of the prism and δ

_{m}➔ angle of minimum deviation. This is known as the prism formula.

3. Which of the following is Cauchy’s formula?

a) μ=A+Bλ^{2}+Cλ^{4}

b) μ=A+\(\frac {B}{\lambda^2} + \frac {C}{\lambda^4}\)

c) μ=A+B+CBλ

d) μ=A+\(\frac {B}{\lambda}+\frac {C}{\lambda^2}\)

View Answer

Explanation: Cauchy’s dispersion formula is an empirical expression that gives an approximate relation between the refractive index of a medium and the wavelength of the light. Cauchy’s formula is given as:

μ=A+\(\frac {B}{\lambda^2} + \frac {C}{\lambda^4}\)

Where A, B, and C are the arbitrary constants of the medium.

4. The Refractive index of a material of a prism is different for different colors.

a) True

b) False

View Answer

Explanation: Yes, this statement is true. The Refractive index is the property of a material. Since δ=(μ-1)A, different colors turn through different angles on passing through the prism. This is the cause of dispersion. Therefore, the refractive index of a material of a prism is different for different colors.

5. What is the difference in a deviation between any two colors called?

a) Linear dispersion

b) Angular dispersion

c) Mean deviation

d) Mean dispersion

View Answer

Explanation: The difference in a deviation between any two colors is known as angular dispersion. Angular dispersion is given as:

δ

_{V}-δ

_{R}=(μ

_{V}-μ

_{R})A

Where μ

_{V}and μ

_{R}are the refractive index for violet rays and red rays, respectively. Mean deviation is δ = \( ( \frac {\delta_V + \delta_R}{2} ) \).

6. Pick out the formula for dispersive power from the following.

a) Dispersive power = \(\frac {mean \, deviation}{angular \, dispersion }\)

b) Dispersive power = mean deviation * angular dispersion

c) Dispersive power = mean deviation + angular deviation

d) Dispersive power = \(\frac {angular \, dispersion}{mean \, deviation}\)

View Answer

Explanation: The formula for dispersive power is given as:

Dispersive power (ω)=\(\frac {Angular \, dispersion (\delta_V-\delta_R)}{Mean \, deviation (\delta)}\)

ω=\(\frac {\mu_V-\mu_R}{\mu-1}\)

Where μ=\(\frac {\mu_V+\mu_R}{2}\) = mean refractive index

7. What is the condition for dispersion without deviation?

a) δ-δ’=0

b) δ+δ’=0

c) δ × δ^{‘}=0

d) \(\frac {\delta}{\delta^{‘}}\)=0

View Answer

Explanation: Consider combining two prisms of refracting angles A and A’, and dispersive powers ω and ω’ respectively in such a way that their refracting angles are reversed concerning each other. For no deviation, the condition is:

δ+δ’=0

So, (μ-1)A+(μ’-1)A’=0 or A’=-\(\frac {(\mu -1)A}{(\mu^{‘}-1)}\)

8. The Refractive index and wavelength are directly proportional to each other.

a) True

b) False

View Answer

Explanation: No, this statement is false. The Refractive index of material and wavelength of color are inversely proportional to each other. For example, the wavelength of the color red is the longest, so the refractive index of the same will be the smallest. Similarly, violet has the greatest refractive index and the shortest wavelength.

9. Calculate the dispersive power of crown glass where μ_{V}=1.456 and μ_{R}=1.414.

a) 0.0096

b) 0.45

c) 0.96

d) 0.096

View Answer

Explanation: Given: The refractive index for violet color = 1.456; Refractive index for red color = 1.414

Required equation ➔

ω=\(\frac {\mu_V – \mu_R}{\mu – 1}\)

Also, μ=\(\frac {(\mu_V+\mu_R)}{2}\)

μ=\(\frac {1.456+1.414}{2}\)=1.435

Thus, ω=\(\frac {1.456-1.414}{1.435-1}\)

ω=\(\frac {0.042}{0.435}\)

ω=0.096

Therefore, the dispersive power of crown glass is 0.096.

10. A thin prism with an angle of 3^{o} and made from glass of refractive index 1.15 is combined with another prism made from glass and has a refractive index of 1.45. If the dispersion were to occur without deviation then what should be the angle of the second prism?

a) 3^{o}

b) 0^{o}

c) 1^{o}

d) 2^{o}

View Answer

Explanation: The required equation ➔ δ=(μ-1)A

When two prisms are combined, then:

δ=δ+δ’=(μ-1)A+(μ’-1)A’=0

So, A’=-\(\frac {(\mu-1)A}{\mu^{‘}-1}\)

A’=-\(\frac {(1.15-1)}{1.45-1}\) × 3

A’=-1

^{o}

Therefore, the angle of the other prism is 1

^{o}and opposite of the first prism.

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