A ray in air is incident on a glass plate whose index of refraction is 1.40. The angle of refraction is one-half the angle of reflection. The angle of refraction is closest to

46⁰

Explanation:

We solve this by using snell's law

n1sinθ1 = nrSinθr

n1 and nr = refractive index of incident medium and also refractive medium

We have that θ1 = θr/2

Such that

1 sin2θr = 1.40Sinθr

Sin2θ = 2sinθcosθ when we use trigonometric identity

2sinθrCosθr = 1.40sinθr

Cosθr = 1.40/2

= 0.7

θr = cos^-1(0.7)

= 45.57⁰

This is approximately 46⁰

the area between the graph and the t axis

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2