A beam of light strikes the flat, glass side of a water-filled aquarium at an angle of 37.5° to the normal. For glass, n = 1.50.
(a) At what angle does the beam enter the glass?
(b) At what angle does the beam enter the water?
To find the angle at which the beam enters the glass, we need to apply the law of reflection and Snell's law.
(a) To find the angle of incidence (θ1) at which the beam enters the glass, we need to use the law of reflection. According to this law, the angle of incidence is equal to the angle of reflection.
So, θ1 = 37.5°.
(b) To find the angle at which the beam enters the water, we need to use Snell's law, which states:
n1*sin(θ1) = n2*sin(θ2),
where n1 and n2 are the indices of refraction of the two mediums, and θ1 and θ2 are the angles of incidence and refraction, respectively.
Given that the index of refraction for glass is 1.50 and assuming the index of refraction for water is 1.33, we can rearrange Snell's law to solve for θ2.
n1*sin(θ1) = n2*sin(θ2),
(1.50)*sin(37.5°) = (1.33)*sin(θ2).
Solving for θ2, we get:
θ2 = sin^(-1)[(1.50*sin(37.5°))/1.33].
Using a calculator, we find that θ2 is approximately 41.83°.
Therefore, the beam enters the glass at an angle of 37.5° and enters the water at an angle of approximately 41.83°.