A ray of light is incident on a quartz plate with a refractive index of 1.54. Determine the angle of incidence

A ray of light is incident on a quartz plate with a refractive index of 1.54. Determine the angle of incidence of the beam, knowing that the angle between the reflected and refracted beam is 90?

Since the angle of incidence α is equal to the angle of refraction (the angle between the reflected β and the refracted rays is 90 degrees, it follows from the condition):

Find the angle of reflection: β = 90 ° – α.

Let’s remember the formula for calculating the refractive index:

sin a / sin β = n.

We substitute the refractive index in the formula instead of β = 90 ° – a and we get:

sin a / sin (90 ° – a) = n.

We transform and calculate:

sin a = n * sin (90 ° – a) = n (sin 90 ° * cos a – cos 90 ° * sina);

sin a = n * cos a;

tg a = n;

a = arctan (n) = arctan 1.54 = 57 °.