Related Problems with Solution
Problem 1 : Reflection and Refraction
Problem Statement: A beam of light traveling in air n1=1 enters a glass block n2=1.5 at an angle of incidence (i) of $$(30^\circ).$$ Calculate the angle of refraction (r) inside the glass block and determine whether total internal reflection occurs at the glass-air interface.
Solution :
- Step 1: Use Snell’s Law to find the angle of refraction $$((r)): (n_1\sin(i) = n_2\sin(r)).$$
- Step 2: Substitute values: $$(1\sin(30^\circ) = 1.5\sin(r)).$$
- Step 3: Solve for $$(r): (r = \sin^{-1}\left(\frac{1}{1.5}\sin(30^\circ)\right)).$$
The angle of refraction ((r)) can be calculated, and it turns out to be (20^\circ). Now, let’s check if total internal reflection occurs:
- Total Internal Reflection Condition: $$(i > \theta_c),$$ where θc is the critical angle.
- Calculate the critical angle: $$(\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right)).$$
- Substitute values: $$(\theta_c = \sin^{-1}\left(\frac{1.5}{1}\right)).$$
Since the angle of incidence $$((i = 30^\circ))$$ is greater than the critical angle $$((\theta_c \approx 48.59^\circ)),$$ total internal reflection does not occur.
