Question

1a. You can determine the index of refraction of a substance by determining its critical angle. What is the index of refraction of a substance that has a critical angle of 62.0° when submerged in water?

1b. What is the substance?

Options: diamond, fluorite, flint glass, ice, plexiglass, crystalline quartz, fused quartz, zircon

1c. What would the critical angle be for this substance in air?

Answer 1

Answer :

Critical angle is the angle of incidence at which the angle of refraction becomes 90° when light travels from more denser medium to less dense medium.

1a.

Given:

• Critical angle :
• Refractive index of water is 1.33

We will take substance as first medium and water as second medium of refraction.

Let,

• be the index of refraction of a substance.
• be the index of refraction of water.

Critical angle is given by,

Therefore,

This is the index of refraction of the substance.

1b.

The substance is plexiglass.

1c.

​​​​​​Now we have to find critical angle when light is passing from this substance into the air. Hence substance becomes first medium of refraction and air becomes second index of refraction. Refractive index of air is 1.00

Let,

• Index of refraction of substance is :
• Index of refraction of air is :

Thus the critical angle is given by,

This is the critical angle for this substance in air.