Related Problems with Solution
Problem 1 : Dispersion Through a Glass Prism
Problem Statement: A ray of white light enters a glass prism at an angle of 45° to the base of the prism. The refractive index of the glass is (1.5). Calculate the angle of deviation for the violet component of the light when it exits the prism.
Solution :
- Step 1: Given values: Angle of incidence θ1 = 45 °,Refractive index ((n)) = (1.5).
- Step 2: Use Snell’s Law to find the angle of refraction θ2 inside the prism: $$(n_1\sin\theta_1 = n_2\sin\theta_2),$$ where n1 is the refractive index of air.
- Step 3: Calculate $$(\theta_2): (1.0 \cdot \sin(45^\circ) = 1.5 \cdot \sin(\theta_2)).$$
- Step 4: Solve for $$(\theta_2): (\sin(\theta_2) = \frac{1}{1.5}).$$
- Step 5: Calculate $$(\theta_2): (\theta_2 = \sin^{-1}\left(\frac{1}{1.5}\right)).$$
- Step 6: Calculate the angle of deviation δ using the prism formula: $$(\delta = A + \epsilon - \alpha),$$ where (A) is the angle of the prism, ε is the angle of deviation, and α is the angle of incidence inside the prism.
- Step 7: Substitute the values: $$(\delta = 60^\circ + \epsilon - 45^\circ).$$
- Step 8: Solve for $$(\epsilon): (\epsilon = \delta - 15^\circ).$$
So, the angle of deviation for the violet component of light is $$(\delta - 15^\circ).$$
