Refraction through a Prism MCQ Quiz - Objective Question with Answer for Refraction through a Prism - Download Free PDF

Calculatiion:

δ_net = 0

(μ₁ – 1)A₁ – (μ2 – 1)A₂ = 0

(1.54 – 1)4 – (1.72 – 1)A₂ = 0

A₂ = 3°

Concept :

When a light ray suffers minimum deviation in a prism, the angle of incidence and the angle of emergence are equal, and the light ray travels symmetrically through the prism. When additional prisms of identical shape and material are added in such a way that the light ray enters and exits at the same angle, the overall deviation remains unchanged.

Calculation:

Given that the prism P causes the ray to suffer minimum deviation:

⇒ Deviation in prism P = δ_min

When additional prisms Q and R are added:

⇒ Deviation in prism Q and R = 0 (since they are identical and arranged symmetrically)

Total deviation = Deviation in P + Deviation in Q + Deviation in R

⇒ Total deviation = δ_min + 0 + 0

∴ Total deviation = δ_min

Hence, the ray will now suffer the same deviation as before.

Concept :

When a light ray suffers minimum deviation in a prism, the angle of incidence and the angle of emergence are equal, and the light ray travels symmetrically through the prism. When additional prisms of identical shape and material are added in such a way that the light ray enters and exits at the same angle, the overall deviation remains unchanged.

Calculation:

Given that the prism P causes the ray to suffer minimum deviation:

⇒ Deviation in prism P = δ_min

When additional prisms Q and R are added:

⇒ Deviation in prism Q and R = 0 (since they are identical and arranged symmetrically)

Total deviation = Deviation in P + Deviation in Q + Deviation in R

⇒ Total deviation = δ_min + 0 + 0

∴ Total deviation = δ_min

Hence, the ray will now suffer the same deviation as before.

Explanation:

• Statement I is correct because, when white light passes through a prism, it disperses into its constituent colors. Red light, having the longest wavelength, bends the least, while violet light, having the shortest wavelength, bends the most.
• As λred > λyellow > λviolet
• Statement II is also correct because the refractive index of a medium varies with the wavelength of light, leading to different bending angles for different colors (this phenomenon is called dispersion).
• A light ray with a longer wavelength bends less. 
• Statement II explains why red light bends less than yellow and violet.

∴ The correct option is 1

Explanation:

Refraction is the bending of light as it passes from one medium to another with different refractive indices.

When light enters a medium with a higher refractive index (such as water) from a medium with a lower refractive index (such as air), the light bends towards the normal.

When light exits a medium with a higher refractive index (such as water) into a medium with a lower refractive index (such as air), the light bends away from the normal.

A prism typically causes light to deviate from its path, and the amount of deviation depends on the angle of incidence, the geometry of the prism, and the refractive indices of the involved media.

In this case, the hollow prism is filled with water, which has a refractive index of about 1.33, while air has a refractive index of approximately 1.00.

When light passes through a hollow prism filled with water, it will experience two refractions:

• First, as light enters the water from air, it bends towards the normal due to the higher refractive index of water (1.33).
• Second, as light exits the water into air, it bends away from the normal because air has a lower refractive index (1.00).

These two bending effects combine and cause the overall deviation of the incident ray to be towards the base of the prism.

∴ The correct answer is option 4) Towards the base.

Calculation:

The formula for the refractive index is given as:

r₁ + c = A

⇒ r₁ = 90 - c

Snell's law at the emergent boundary

Sin(c) = 1 / μ

⇒ Cos(c) = (μ² - 1)^1/2 / μ

According to Snell's law at incident boundary

Sin(30) = μ × Sin(r₁)

1/2 = μ × Sin(90 - c) =μ Cos(c)

⇒ 1/2 = μ × (μ² - 1)^1/2 / μ

Squaring both sides:

1/4 = μ² - 1

μ² = 5 / 4

μ = √(5 / 4) = √5 / 2

Thus, the correct option is option 2: μ = √5 / 2

CONCEPT

The critical angle in optics refers to a specific angle of incidence. Beyond this angle, the total internal reflection of light will occur.

\(n_i\times sinθ_i = n_r\times sinθ_r\)

When θ_r becomes 90^o then the angle of incidence is called the critical angle of incidence. θ_cr

\(n_i\times sinθ_{cr} = n_r \times sin90^o\)

\(\Rightarrow n_i \times sinθ_{cr} = n_r\)

Where n_r = refractive index of the medium, n_i = refractive index of air (Rarer medium) (1)

if the angle of incidence of greater than the critical angle of incidence then the light rays get reflected back this phenomenon is called total internal reflection and the material becomes non-transparent.

CALCULATION:

Case 1) when n_r = 1.33 and θ = 48.75^o

\(n_i \times simθ = 1.33\)

\(θ = sin^{-1}(\frac{1}{1.33})\)

θ_cr = 48.753° 

In this case, water will be a transparent media.

Case 2) when n_r = 1.12,  θ = 29.4^o

Calculation of critical angle for crown glass

\(θ_{cr} = sin^{-1}(\frac{1}{1.12})\)

θ_cr = 63.23^o

θ_cr > 29.4° 

therefore crown glass will be transparent 

Case 3) when n_r = 1.62 and θ = 37.31⁰

Calculation of critical angle for dense flint glass

\(θ_{cr} = sin^{-1}(\frac{1}{1.62})\)

θ_cr = 38.11^o

θ_cr > 37.31^o

therefore dense flint glass will also be transparent.

Case 4) when n_r = 2.42 and θ = 24.41

Calculation of critical angle for diamond

\(θ_{cr} = sin^{-1}(\frac{1}{2.42})\)

θ_cr = 24.40^o

θ_cr < 24.41° 

In this case, the critical angle is less than the incident angle therefore the light rays will reflect back.

Calculation:

The formula for the refractive index is given as:

r₁ + c = A

⇒ r₁ = 90 - c

Snell's law at the emergent boundary

Sin(c) = 1 / μ

⇒ Cos(c) = (μ² - 1)^1/2 / μ

According to Snell's law at incident boundary

Sin(30) = μ × Sin(r₁)

1/2 = μ × Sin(90 - c) =μ Cos(c)

⇒ 1/2 = μ × (μ² - 1)^1/2 / μ

Squaring both sides:

1/4 = μ² - 1

μ² = 5 / 4

μ = √(5 / 4) = √5 / 2

Thus, the correct option is option 2: μ = √5 / 2

Explanation:

• Statement I is correct because, when white light passes through a prism, it disperses into its constituent colors. Red light, having the longest wavelength, bends the least, while violet light, having the shortest wavelength, bends the most.
• As λred > λyellow > λviolet
• Statement II is also correct because the refractive index of a medium varies with the wavelength of light, leading to different bending angles for different colors (this phenomenon is called dispersion).
• A light ray with a longer wavelength bends less. 
• Statement II explains why red light bends less than yellow and violet.

∴ The correct option is 1

Calculatiion:

δ_net = 0

(μ₁ – 1)A₁ – (μ2 – 1)A₂ = 0

(1.54 – 1)4 – (1.72 – 1)A₂ = 0

A₂ = 3°

Concept :

When a light ray suffers minimum deviation in a prism, the angle of incidence and the angle of emergence are equal, and the light ray travels symmetrically through the prism. When additional prisms of identical shape and material are added in such a way that the light ray enters and exits at the same angle, the overall deviation remains unchanged.

Calculation:

Given that the prism P causes the ray to suffer minimum deviation:

⇒ Deviation in prism P = δ_min

When additional prisms Q and R are added:

⇒ Deviation in prism Q and R = 0 (since they are identical and arranged symmetrically)

Total deviation = Deviation in P + Deviation in Q + Deviation in R

⇒ Total deviation = δ_min + 0 + 0

∴ Total deviation = δ_min

Hence, the ray will now suffer the same deviation as before.

Explanation:

Refraction is the bending of light as it passes from one medium to another with different refractive indices.

When light enters a medium with a higher refractive index (such as water) from a medium with a lower refractive index (such as air), the light bends towards the normal.

When light exits a medium with a higher refractive index (such as water) into a medium with a lower refractive index (such as air), the light bends away from the normal.

A prism typically causes light to deviate from its path, and the amount of deviation depends on the angle of incidence, the geometry of the prism, and the refractive indices of the involved media.

In this case, the hollow prism is filled with water, which has a refractive index of about 1.33, while air has a refractive index of approximately 1.00.

When light passes through a hollow prism filled with water, it will experience two refractions:

• First, as light enters the water from air, it bends towards the normal due to the higher refractive index of water (1.33).
• Second, as light exits the water into air, it bends away from the normal because air has a lower refractive index (1.00).

These two bending effects combine and cause the overall deviation of the incident ray to be towards the base of the prism.

∴ The correct answer is option 4) Towards the base.

CONCEPT

The critical angle in optics refers to a specific angle of incidence. Beyond this angle, the total internal reflection of light will occur.

\(n_i\times sinθ_i = n_r\times sinθ_r\)

When θ_r becomes 90^o then the angle of incidence is called the critical angle of incidence. θ_cr

\(n_i\times sinθ_{cr} = n_r \times sin90^o\)

\(\Rightarrow n_i \times sinθ_{cr} = n_r\)

Where n_r = refractive index of the medium, n_i = refractive index of air (Rarer medium) (1)

if the angle of incidence of greater than the critical angle of incidence then the light rays get reflected back this phenomenon is called total internal reflection and the material becomes non-transparent.

CALCULATION:

Case 1) when n_r = 1.33 and θ = 48.75^o

\(n_i \times simθ = 1.33\)

\(θ = sin^{-1}(\frac{1}{1.33})\)

θ_cr = 48.753° 

In this case, water will be a transparent media.

Case 2) when n_r = 1.12,  θ = 29.4^o

Calculation of critical angle for crown glass

\(θ_{cr} = sin^{-1}(\frac{1}{1.12})\)

θ_cr = 63.23^o

θ_cr > 29.4° 

therefore crown glass will be transparent 

Case 3) when n_r = 1.62 and θ = 37.31⁰

Calculation of critical angle for dense flint glass

\(θ_{cr} = sin^{-1}(\frac{1}{1.62})\)

θ_cr = 38.11^o

θ_cr > 37.31^o

therefore dense flint glass will also be transparent.

Case 4) when n_r = 2.42 and θ = 24.41

Calculation of critical angle for diamond

\(θ_{cr} = sin^{-1}(\frac{1}{2.42})\)

θ_cr = 24.40^o

θ_cr < 24.41° 

In this case, the critical angle is less than the incident angle therefore the light rays will reflect back.

Calculation:

By using optical reversibility principle.

For prism P₂

→ Minimum deviation

\(1 \times \sin \theta_{1}=\sqrt{3} \sin r \quad r_{1}=r_{2}=\frac{A}{2}\)

\(\sin \theta_{1}=\sqrt{3} \times \frac{1}{2} \quad r_{1}=r_{2}=30^{\circ}\)

⇒ i = e = 60°

For prism P₁

Incident angle will be 60°

\(1 \times \sin 60^{\circ}=\frac{\sqrt{3}}{\sqrt{2}} \sin r_{1}\)

\(\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{\sqrt{2}} \sin r_{1}\)

r₁ + r₂ = 60° 

\(\sin r_{1}=\frac{1}{\sqrt{2}}\)

r₁ = 45° 

r2 = 15° 

\(\frac{\sqrt{3}}{\sqrt{2}} \sin \left(45^{\circ}\right)=1 \times \sin \theta\)

\(15^{\circ}=\frac{\pi \times 15}{180} \mathrm{rad}=\frac{\pi}{12} \mathrm{rad}\)

\(\theta=\sin ^{-1}\left[\frac{\sqrt{3}}{\sqrt{2}} \sin \left(\frac{\pi}{12}\right)\right]\)

β = 12

Concept :

When a light ray suffers minimum deviation in a prism, the angle of incidence and the angle of emergence are equal, and the light ray travels symmetrically through the prism. When additional prisms of identical shape and material are added in such a way that the light ray enters and exits at the same angle, the overall deviation remains unchanged.

Calculation:

Given that the prism P causes the ray to suffer minimum deviation:

⇒ Deviation in prism P = δ_min

When additional prisms Q and R are added:

⇒ Deviation in prism Q and R = 0 (since they are identical and arranged symmetrically)

Total deviation = Deviation in P + Deviation in Q + Deviation in R

⇒ Total deviation = δ_min + 0 + 0

∴ Total deviation = δ_min

Hence, the ray will now suffer the same deviation as before.