Aray of light traveling through air is incident on the smooth flat slab of crown glass at an angle of 30 to the normal.take the refracted index of crown glass as l.52. find ( a) angle of refraction, (b) critical angle between air to crown glass
To find the answers to your questions, we can use Snell's Law, which describes the relationship between the angles of incidence and refraction and the refractive indices of the materials involved.
a) To find the angle of refraction, we can start by using Snell's Law, which states that the ratio of the sine of the angle of incidence (θ₁) to the sine of the angle of refraction (θ₂) is equal to the ratio of the refractive indices (n₁ and n₂) of the two mediums:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
In this case, the incident angle (θ₁) is given as 30°, and the refractive index of the crown glass (n₂) is given as 1.52. Since the light is traveling from air (which has a refractive index of approximately 1) to crown glass, n₁ is 1. Applying these values to Snell's Law, we can solve for θ₂:
1 * sin(30°) = 1.52 * sin(θ₂)
sin(30°) = 1.52 * sin(θ₂)
Using a scientific calculator or trigonometric tables, we can find the value of sin(θ₂) by solving for θ₂:
θ₂ ≈ sin^⁻¹(sin(30°) / 1.52)
By calculating this expression, we find that θ₂ ≈ 19.75°. Therefore, the angle of refraction is approximately 19.75°.
b) The critical angle occurs when the angle of refraction becomes 90°. At this angle, the refracted light travels along the boundary between the two mediums, instead of passing through the interface. We can use the inverse of Snell's Law to find the critical angle:
sin(θ_c) = n₂ / n₁
If we substitute the refractive indices into the equation, we can solve for θ_c:
sin(θ_c) = 1.52 / 1
θ_c = sin^⁻¹(1.52)
Using a calculator or trigonometric tables, we can find that θ_c ≈ 61.16°. Therefore, the critical angle between air and crown glass is approximately 61.16°.