Question

Suppose you have an unknown clear substance immersed in water, and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of 45.0°, and you observe the angle of refraction to be 40.3°. What is the index of refraction of the substance and its likely identity?

a) Index of refraction = (1.22), likely identity = Water
b) Index of refraction = (1.50), likely identity = Glass
c) Index of refraction = (1.67), likely identity = Diamond
d) Index of refraction = (1.82), likely identity = Plastic

Answer 1

The index of refraction of the unknown substance is approximately 1.50 and its likely identity is Glass.

Step-by-step explanation:

To find the index of refraction of the unknown substance, we can use Snell's Law. Snell's Law relates the angle of incidence and the angle of refraction to the indices of refraction of the two media. The formula is:

n1*sin(angle of incidence) = n2*sin(angle of refraction)

In this case, the medium is water and the angle of incidence is 45.0°, and the angle of refraction is 40.3°. We can plug these values into the formula and solve for the index of refraction of the unknown substance:

1.333*sin(45.0°) = n2*sin(40.3°)

Solving for n2, we get:

n2 = 1.333*sin(45.0°) / sin(40.3°) ≈ 1.50

The index of refraction of the unknown substance is approximately 1.50. Based on the options provided, the likely identity of the substance is Glass.