Calculating the Refraction Angle of a Light Ray Incident on a Prism

[BioMechanical]

Homework Statement

A light ray is incident on a prism whose apex angle is 65.0°. The ray is
incident at θa and leaves the prism with θa = θd. The refractive index of
the prism glass is 1.54.
Calculate θ



ans:55.8°

Homework Equations

n1sin$$\phi$$1=n2sin$$\phi$$2

The Attempt at a Solution

please help

 

[astrorob]

See attachment before reading.

If the apex angle is 65 degrees, that means that our base angles are x = (180-65) / 2 = 57.5 degrees.

Now we know that the angle that the light enters the prism is equal to the angle that it leaves, this is another way of saying that the light travels parallel to the base of the prism. By simple trigonometry, we can determine angle θ2. Remember, θ2 is measured relative to the normal of incidence, N.(perpendicular to incident surface of prism).

θ2 = 90 - 57.5 = 32.5 degrees.

Once this is determined, we need to use Snell's law.

We've just found θ2 through geometry, and we're after θ1.

Regards,
Rob.

 

[BioMechanical]

ohhh i get it. Thanks a lot.