Question

A plate of glass with parallel faces having a refractive index of 1.58 is resting on the surface of water in a tank. A ray of light coming from above in air makes an angle of incidence 38.0° with the normal to the topsurface of the glass.

What angle θ does the ray refracted into thewater make with the normal to the surface? Use 1.33 for the indexof refraction of water.

Express your answer in degrees.

Answer 1

Concepts and reason

The concept used to solve this problem is Snell’s law of refraction.

First, use the Snell’s law to find the refracted angle from the glass and to the water.

Then use the concepts of Snell’s law using the relation between the refractive index of the two medium and incident rays, to calculate the refracted angle.

Fundamentals

Snell’s law deals with the relationship between the refracted angle and incident angle.

First consider the region 1 that consists of air and glass medium:

Apply the Snell’s law in the region 1 as given below:

Here, is the refractive index of air, is the refractive index of glass, is the incident angle of the ray in region 1, and is the refracted angle of the ray in region 1.

Now consider the region 2 that consists of glass and water medium:

Apply the Snell’s law in the region 2,

Here, is the refractive index of water, is the incident angle of the ray in region 2, and is the refracted angle of the ray in region 2.

Apply the Snell’s law in the region 1,

Rearrange the above equation to get .

Substitute for , for , and for .

Apply the Snell’s law in the region 2,

Rearrange the above equation to get ,

Substitute for , for , and for .

Ans:

Thus, the angle at which the ray enters into the water is .

Answer 2