A beam of light enters a prism with an angle of 60 degrees. If the refractive index of the prism is 1.5, what is the angle of refraction inside the prism?
Practice Questions
1 question
Q1
A beam of light enters a prism with an angle of 60 degrees. If the refractive index of the prism is 1.5, what is the angle of refraction inside the prism?
30 degrees
45 degrees
60 degrees
90 degrees
Using Snell's law, sin(θ2) = sin(60)/1.5, we find θ2 = 30 degrees.
Questions & Step-by-step Solutions
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Q
Q: A beam of light enters a prism with an angle of 60 degrees. If the refractive index of the prism is 1.5, what is the angle of refraction inside the prism?
Solution: Using Snell's law, sin(θ2) = sin(60)/1.5, we find θ2 = 30 degrees.
Steps: 10
Step 1: Understand that when light enters a new medium (like a prism), it bends. This bending is described by Snell's law.
Step 2: Snell's law states that n1 * sin(θ1) = n2 * sin(θ2), where n is the refractive index and θ is the angle.
Step 3: In this case, the light is entering the prism from air. The refractive index of air (n1) is approximately 1.0, and the refractive index of the prism (n2) is 1.5.
Step 4: The angle of incidence (θ1) is given as 60 degrees.
Step 5: Plug the values into Snell's law: 1.0 * sin(60 degrees) = 1.5 * sin(θ2).
Step 6: Calculate sin(60 degrees), which is √3/2 or approximately 0.866.
Step 7: Rewrite the equation: 0.866 = 1.5 * sin(θ2).
Step 8: To find sin(θ2), divide both sides by 1.5: sin(θ2) = 0.866 / 1.5.
Step 9: Calculate 0.866 / 1.5, which is approximately 0.577.
Step 10: Now, find θ2 by taking the inverse sine (arcsin) of 0.577, which gives approximately 30 degrees.
