A beam of light falls on a glass plate in the air. Refractive index of glass n = 1.5. The angle between the refracted

A beam of light falls on a glass plate in the air. Refractive index of glass n = 1.5. The angle between the refracted and reflected rays is 90 °. Determine the angle of incidence

The beam falls and is reflected from the plate at an angle a. The angle of refraction is equal to the difference:
b = 180 – a – 90 ° = 90 ° – a.
Snell’s law for incident and reflected rays:
sin a / sin (90 – a) = n, where n is the refractive index of the glass.
sin a = 1.5 sin (90 ° – a).
Casting formula:
sin (90 – a) = cos a;
sin a = 1.5 cos a;
sin a / cos a = tg a = 1.5.
According to the table of tangents, we find the angle of incidence a:
arctan a = 56.3 °.
Answer: The angle of incidence is 56.3 °.