A ray of light passing through an equilateral prism is having velocity 2.12 x 10^8 m/s in the prism material, then the minimum angle of deviation is _______ degrees.

The correct answer is Option 2. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q40 – JEE-MAIN 2026

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Home Physics Ray OpticsQuestion #406

A ray of light passing through an equilateral prism is having velocity

2.12 \times 10^{8}

m/s in the prism material, then the minimum angle of deviation is _______ degrees.

Clue 1 of 3: Refractive Index and Prism Geometry

Understand how the speed of light in a medium relates to its refractive index, and recall that an equilateral prism has a prism angle of $60^{\circ}$ .

🧠 Full Solution Path

● Video Walkthrough

Step 1: Calculate the Refractive Index✦ Active

The refractive index $n$ of the prism material is given by the ratio of the speed of light in vacuum ( $c = 3 \times 10^{8}$ m/s) to the speed of light in the prism material ( $v = 2.12 \times 10^{8}$ m/s).

n = \frac{c}{v} = \frac{3 \times 10^{8} m/s}{2.12 \times 10^{8} m/s} \approx 1.415

Step 2: Apply the Minimum Deviation Formula○ Expand

For a prism, the refractive index $n$ is related to the prism angle $A$ and the minimum angle of deviation $δ_{m}$ by the formula:

n = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin (\frac{A}{2})}

For an equilateral prism, the prism angle $A = 60^{\circ}$ . Substituting the values:

1.415 = \frac{\sin (\frac{60^{\circ} + δ_{m}}{2})}{\sin (\frac{60^{\circ}}{2})} = \frac{\sin (\frac{60^{\circ} + δ_{m}}{2})}{\sin (30^{\circ})}

💡 Teacher's Secret Hint

Recall that $\sin (30^{\circ}) = 0.5$ .

Step 3: Solve for Minimum Deviation○ Expand

Substitute $\sin (30^{\circ}) = 0.5$ into the equation from Step 2:

1.415 = \frac{\sin (\frac{60^{\circ} + δ_{m}}{2})}{0.5}

Rearranging to solve for the sine term:

\sin (\frac{60^{\circ} + δ_{m}}{2}) = 1.415 \times 0.5 = 0.7075

We know that $\sin (45^{\circ}) \approx 0.7071$ . Therefore:

\frac{60^{\circ} + δ_{m}}{2} \approx 45^{\circ}

Solving for $δ_{m}$ :

60^{\circ} + δ_{m} = 90^{\circ}

δ_{m} = 90^{\circ} - 60^{\circ} = 30^{\circ}

💡 Teacher's Secret Hint

Remember the common trigonometric values for angles like $30^{\circ}$ and $45^{\circ}$ .

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Physics Question 40 – JEE-MAIN 2026

Clue 1 of 3: Refractive Index and Prism Geometry

🧠 Full Solution Path