The critical angle for a transparent material in air is 30 degrees. The index of refraction of the material is most nearly

A) 0.33
B) 0.50
D) 1.5
E) 2.0

2.0

To find the index of refraction of a transparent material, we can use the formula:

n = 1 / sin(critical angle),

where n is the index of refraction and the critical angle is given as 30 degrees.

Plugging in the values:

n = 1 / sin(30°).

Using a calculator, we find:

n ≈ 1.732.

Among the given options, the index of refraction that is closest to 1.732 is 1.5.

Therefore, the most nearly correct answer is D) 1.5.

To determine the index of refraction of the transparent material, we can use the formula for the critical angle, which is given by:

sin(critical angle) = 1 / refractive index

In this case, the critical angle is given as 30 degrees. We can convert this to radians by multiplying by π/180:

sin(30°) = sin(π/6)

Now, we can rearrange the formula and solve for the refractive index:

refractive index = 1 / sin(critical angle)

refractive index = 1 / sin(π/6)

Using a calculator, we can find that sin(π/6) ≈ 0.5. Thus,

refractive index ≈ 1 / 0.5

refractive index ≈ 2.0

Therefore, the index of refraction of the transparent material is most nearly 2.0. The correct option is E) 2.0.