A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. The angle of minimum deviation is measured to be $40^\circ$. What is the refractive index of the material of the prism? The refracting angle of the prism is $60^\circ$. If the prism is placed in water (refractive index $1.33$), predict the new angle of minimum deviation of a parallel beam of light.

A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the pr

Exercises · 9.6

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Using the prism formula $n=\frac{\sin[(A+\delta_m)/2]}{\sin(A/2)}$ with $A=60^\circ$ and $\delta_m=40^\circ$ , the refractive index of the glass is $n_g\approx1.53$ . When the prism is immersed in water ( $n_w=1.33$ ), the effective (relative) refractive index becomes $n_{rel}=n_g/n_w\approx1.15$ , and the new angle of minimum deviation is $\delta_m'\approx10.3^\circ$ .

Step 1 — refractive index of the glass in air

n_g = \frac{\sin\left(\frac{A+\delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)} = \frac{\sin 50^\circ}{\sin 30^\circ} = \frac{0.766}{0.5} = 1.532

Step 2 — relative refractive index in water

The prism formula's $n$ is always the refractive index of the prism relative to the surrounding medium. In water, that relative index is

n_{rel} = \frac{n_g}{n_w} = \frac{1.532}{1.33} \approx 1.152

Step 3 — new angle of minimum deviation

Using the prism formula again, now with $n_{rel}$ in place of $n_g$ , and the same prism angle $A=60^\circ$ :

$n_{rel} = \frac{\sin\left(\frac{A+\delta_m'}{2}\right)}{\sin(A/2)} \;\Rightarrow\; \sin\left(\frac{A+\delta_m'}{2}\right) = 1.152 \times 0.5 = 0.576$ …

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Here are the common mistakes students make on this classic prism problem, along with how to avoid each one.

1. Forgetting the Formula for Refractive Index

Mistake:

Students often try to guess or derive the refractive index without using the standard formula:

\mu = \frac{\sin\left(\frac{A + \delta_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}

They might incorrectly use $\mu = \frac{\sin i}{\sin r}$ directly without linking it to the prism geometry.

How to avoid:

Memorise the prism formula as a standard result.
Always write it down first before plugging numbers.
Remember: $A$ is the refracting angle (given as $60^\circ$ ), and $\delta_m$ is the angle of minimum deviation ( $40^\circ$ ).

2. Incorrect Substitution of Angles

Mistake:

Students sometimes substitute $A = 60^\circ$ and $\delta_m = 40^\circ$ directly into the formula without computing the half-angles correctly.

Example of error:

Writing $\sin(60^\circ + 40^\circ)$ instead of $\sin\left(\frac{60^\circ + 40^\circ}{2}\right)$ .

How to avoid:

Always compute the half-sum first:

\frac{A + \delta_m}{2} = \frac{60^\circ + 40^\circ}{2} = 50^\circ

Then compute $\sin 50^\circ$ and $\sin 30^\circ$ separately.

3. Using Degrees in Calculator Without Checking Mode

Mistake:

Many students forget to set their calculator to degree mode when evaluating $\sin 50^\circ$ and $\sin 30^\circ$ , leading to wildly wrong answers.

How to avoid:

Always check the calculator mode before starting.
If you get a refractive index like $0.5$ or $2.5$ , you’ve likely used radians by mistake.

4. Forgetting to Change the Medium for the Second Part

Mistake:

When the prism is placed in water, students often use the same formula with the same $\mu$ for glass, ignoring that the relative refractive index changes.

How to avoid:

The refractive index of glass relative to water is:

\mu_{\text{glass/water}} = \frac{\mu_{\text{glass}}}{\mu_{\text{water}}}

Use this relative index in the prism formula to find the new $\delta_m$ .

5. Assuming the Angle of Minimum Deviation Stays the Same

Mistake:

Some students think $\delta_m$ is a property of the prism alone and doesn’t change with the surrounding medium.

How to avoid:

Understand that $\delta_m$ depends on the relative refractive index between prism and surrounding medium.
When the surrounding medium changes, the bending of light changes, so $\delta_m$ changes.

6. Arithmetic Errors in the Second Part

Mistake: …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

Showing the 12 most recent of 29 on this concept.

CBSE 2026Set A1 markMCQ
$Q.The refractive index of water is 1.33. What will be the speed of light in water? (A) 1.33 × 10^8 m/s (B) 4 × 10^8 m/s (C) 2.25 × 10^8 m/s (D) 3 × 10^8 m/s$
›Reveal solutionSolution

Speed in a medium = c/n = (3 × 10⁸)/1.33 ≈ 2.25 × 10⁸ m/s.

The refractive index of a medium is the ratio of the speed of light in vacuum to that in the medium:

$n=\frac{c}{v}\quad\Rightarrow\quad v=\frac{c}{n}$

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q.The refractive indices of glass and water with respect to air are 3/2 and 4/3, respectively. The refractive index of glass w.r.t. water will be$
(a) 8/9
(b) 9/8
(c) 7/6
(d) 6/7
›Reveal solutionSolution

$n_{g/w} = n_{g/a}/n_{w/a} = (3/2)/(4/3) = 9/8$ .

Refractive index of glass w.r.t. water can be obtained by combining the refractive indices w.r.t. air:

…

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CBSE 2026Set ANNUAL1 markMCQ
$Q.Refraction takes place due to$
(a) change in the speed of light
(b) no change in the speed of light
(c) change in the colour of light
(d) polarization
›Reveal solutionSolution

Light bends when it crosses into a medium where its speed is different; that speed change is the fundamental cause of refraction.

When light travels from one medium into another (e.g. air into glass), its speed changes because the two media have different optical densities (different refractive indices). According to Snell's law, n1sin(theta1) = n2sin(theta2), and refractive index n = c/v (speed of light in vacuum divided by speed in the medium). Because the speed v changes at the boundary, the direction of the light ray bends - this bending is refraction. If the speed did no …

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CBSE 2026Set ANNUAL1 markMCQ
$Q. The optical density of turpentine is higher than that of water while its mass density is lower. Figure shows a layer of turpentine floating over water in a container. Which of the following four rays incident on turpentine in figure, the path shown is correct?$
(a) 1
(b) 2
(c) 3
(d) 4
›Reveal solutionSolution
Since turpentine is optically the densest of the three (n(turpentine) > n(water) > n(air)), a ray must bend toward the normal at the air–turpentine surface, then bend away from the normal (but not all the way back) at the turpentine–water surface.

The question states the optical density (refractive index) order is turpentine > water > air (even though turpentine's mass density is lower than water's, which is why it floats — optical density and mass density are unrelated). Refraction at each interface follows Snell's law, $n_1\sin\theta_1 = n_2\sin\theta_2$ :

Air → Turpentine: going into an optically denser medium, the ray bends towards the normal (angle decreases).

Turpentine → Water: water is rarer than turpentine, so going into it the ray bends away from the normal (angle increases) compared to its path inside turpentine. …
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CBSE 2026Set ANNUAL1 mark
$Q.In phenomenon of refraction of light, which property of it remains unchanged ?$
›Reveal solutionSolution

In refraction, frequency stays constant; speed and wavelength change.

When light travels from one medium into another, its speed changes (v = c/n) and consequently its wavelength changes (λ = v/f). However, the frequency f is determined by the source of light and does not change when the wave crosses the boundary — the number of wavefronts arriving per second must equal the number leaving per second ( …

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CBSE 2025Set ANNUAL1 mark
$Q.Write Snell's law of refraction.$
›Reveal solutionSolution

Snell's law relates the angle of incidence and angle of refraction at a boundary between two media through a constant called the refractive index.

Snell's law of refraction states that when light passes from one medium into another, the ratio of the sine of the angle of incidence $i$ to the sine of the angle of refraction $r$ is a constant for the given pair of media, called the refractive index of the second medium with respect to the first:

$n_{21} = \dfrac{\sin i}{\sin r} = \dfrac{n_2}{n_1}$

Equivalently, in the symmetric form: $n_1 \sin i = n_2 \sin r$ .

…

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CBSE 2025Set ANNUAL1 markMCQ
$Q.The time taken by the light ray to pass through a glass slab of thickness 5 mm and refractive index μ = 1.5 will be$
(a) 0.25×10⁻¹¹ s
(b) 0.2×10⁻¹⁰ s
(c) 2.5×10⁻¹¹ s
(d) 15×10⁻¹¹ s
›Reveal solutionSolution

Speed of light inside the slab is c/μ; time = thickness ÷ (c/μ).

Speed of light in the glass slab: $v = c/\mu$ . Time taken to cross thickness $d = 5\,mm = 5\times10^{-3}\,m$ : …

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CBSE 2025Set ANNUAL1 markMCQ
$Q.For light incident from air on a slab of refractive index 2, the maximum possible angle of refraction is :$
(a) 60°
(b) 30°
(c) 90°
(d) 45°
›Reveal solutionSolution

At grazing incidence ( $i=90°$ ), Snell's law with $n=2$ gives the maximum possible angle of refraction, $r=30°$ .

Working

For light entering a medium of refractive index $n=2$ from air, Snell's law gives

$\sin i = n\sin r \ \Rightarrow\ \sin r = \dfrac{\sin i}{n}$

…

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CBSE 2025Set ANNUAL1 mark
$Q.The refractive indices of glass and water with respect to air are 3/2 and 4/3 respectively. What will be the refractive index of glass with respect to water ?$
›Reveal solutionSolution

Using $^{a}n_g$ and $^{a}n_w$ , the refractive index of glass relative to water is their ratio: $^{w}n_g = {}^{a}n_g/{}^{a}n_w = 9/8$ .

Given: refractive index of glass w.r.t. air, $^{a}n_g = 3/2$ ; refractive index of water w.r.t. air, $^{a}n_w = 4/3$ .

Refractive index of medium 2 with respect to medium 1 can be written as

$^{1}n_2 = \dfrac{{}^{a}n_2}{{}^{a}n_1}$

…

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CBSE 2024Set ANNUAL1 markMCQ
$Q.The velocity of light in a glass block of refractive index 1.5 is -$
(a) $1.5 \times 10^8\ ms^{-1}$
(b) $2 \times 10^8\ ms^{-1}$
(c) $3 \times 10^8\ ms^{-1}$
(d) $2 \times 10^9\ ms^{-1}$
›Reveal solutionSolution

$v=c/n$ .

The speed of light in a medium of refractive index $n$ is $v = \dfrac{c}{n}$ :

…

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CBSE 2024Set ANNUAL1 markMCQ
$Q. When a ray of light enters a glass slab, then$
(a) its frequency and velocity change.
(b) only frequency changes
(c) its frequency and wavelength changes
(d) its frequency does not change.
›Reveal solutionSolution

When light passes from one medium to another, only its speed and wavelength change; the frequency stays fixed because it is determined by the source that produced the light.

When a light ray crosses from air into a glass slab, the medium's refractive index $n$ slows the wave down: $v = c/n$ . Since $v=f\lambda$ and $f$ cannot change (frequency corresponds to the number of oscillations per second of the source, which is unaffected by what medium the wave later travels through — this is a fundamental result of the wave's boundary conditions at an interface), the wavelength must adjust: $\lambda = v/f = (c/n)/f$ , i.e. wavelength decreases in the denser medium (glass) since $v$ decreases.

…

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CBSE 2023Set B1 mark
$Q. Fill in the blank: The velocity of light ______ when it goes from rare medium to denser medium.$
›Reveal solutionSolution

Speed of light is inversely related to the refractive index of the medium; a denser medium has a higher refractive index and hence a lower light speed.

The refractive index of a medium is defined as $n = c/v$ , where $c$ is the speed of light in vacuum and $v$ is its speed in the medium. An optically denser medium has a higher refractive index, which by this relation means light travels slower in it. So as light passes from a rarer medium (e.g., air) into a denser medium (e.g., glass or water), its spee …

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Concept understanding — Refraction and Snell's Law

Refraction and Snell's Law

Step 1 — refractive index of the glass in air

Step 2 — relative refractive index in water

Step 3 — new angle of minimum deviation

Method: Prism Formula (Minimum Deviation)

Step 1: Recall the Prism Formula

Step 2: Find refractive index in air

Step 3: For prism in water — use relative refractive index

Step 4: Apply prism formula again for new $D_m'$

1. Forgetting the Formula for Refractive Index

2. Incorrect Substitution of Angles

3. Using Degrees in Calculator Without Checking Mode

4. Forgetting to Change the Medium for the Second Part

5. Assuming the Angle of Minimum Deviation Stays the Same

6. Arithmetic Errors in the Second Part

Step 1 — refractive index of the glass in air

Step 2 — relative refractive index in water

Step 3 — new angle of minimum deviation

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