Question

A thin prism has an angle of \(8^{\circ}\) and a minimum deviation of \(6^{\circ}\). Find the speed of light in the prism.

• A. \(1.71\times10^{8}\,m/s,\)
• B. \(2.0\times10^{8}\,m/s\)
• C. \(2.5\times10^{8}\,m/s\)
• D. \(3.0\times10^{8}\,m/s\)

Hint:

For a thin prism, always remember: \[ \boxed{\mu=1+\frac{\delta_m}{A}} \] where both \(A\) and \(\delta_m\) must be in the same unit (degrees or radians). The speed of light inside the prism is \[ \boxed{v=\frac{c}{\mu}}. \]

Answer 1

The Correct Option is A

Concept: A prism is a transparent optical medium that refracts light. For a

thin prism, the refractive index is related to the prism angle and the angle of minimum deviation by \[ \boxed{\mu=1+\frac{\delta_m}{A}} \] where \[ \mu=\text{Refractive index of the prism}, \] \[ A=\text{Angle of the prism}, \] \[ \delta_m=\text{Angle of minimum deviation}. \] Once the refractive index is known, the speed of light inside the prism is obtained using \[ \boxed{\mu=\frac{c}{v}}, \] where \[ c=3\times10^{8}\,m/s \] is the speed of light in vacuum and \[ v=\text{Speed of light inside the prism}. \] Hence, \[ \boxed{v=\frac{c}{\mu}}. \]

Step 1: Write the given data.
Given, \[ A=8^{\circ}, \] \[ \delta_m=6^{\circ}. \] Also, \[ c=3\times10^{8}\,m/s. \]

Step 2: Calculate the refractive index of the prism.
For a thin prism, \[ \mu=1+\frac{\delta_m}{A}. \] Substituting the given values, \[ \mu = 1+\frac{6}{8}. \] Simplifying, \[ \mu = 1+0.75 = 1.75. \] Thus, \[ \boxed{\mu=1.75.} \]

Step 3: Find the speed of light inside the prism.
Using, \[ v=\frac{c}{\mu}, \] we get \[ v = \frac{3\times10^{8}} {1.75}. \] Dividing, \[ v = 1.714\times10^{8}\,m/s. \] Therefore, \[ \boxed{v\approx1.71\times10^{8}\,m/s.} \]

Step 4: Compare the calculated value with the given options.
The calculated speed of light is \[ \boxed{1.71\times10^{8}\,m/s,} \]