Light in air strikes a glass pane with n = 1.51, making a 40 angle with respect

Question

Light in air strikes a glass pane with n = 1.51, making a 40 angle with respect to the normal.

Part A

What angle does the light make with the normal in the glass?

Express your answer to two significant figures and include the appropriate units.

Part B

The glass is 2.1 mm thick. As you know, the ray emerging from the glass is parallel to the ray that entered the glass. Find the perpendicular distance between those parallel rays.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

By Snell's Law

n(air) * sin(40°) = n(glass) * sin(x)
1.00 * sin(40°) = 1.51 * sin(x)

since you are working with 3 significant digits
1.00 * sin(40°) = 1.51 * sin (x)
x is the angle of the light as it travels through the glass.

=> sin(x) = 0.425

=> x = 25.15 degree
Use the Tangent function to calculate the base of the right triangle with a height of 2.1 mm and an angle of x .

Tangent function = opposite/adjacent
tan (x) = opposite/2.1 mm

Since the ray will resume it's original angle when it leaves the glass, the length of the base (opposite) of the triangle will be the perpendicular distance between the parallel rays.

=> opposite = 0.985 mm

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