Your eye is designed to work in air. Surrounding it with water impairs its abili

Question

Your eye is designed to work in air. Surrounding it with water impairs its ability to form images. Consequently, scuba divers wear masks to allow them to form images properly underwater. However, this does affect the perception of distance, as you will calculate.

Consider a flat piece of plastic (index of refraction ) with water (index of refraction ) on one side and air (index of refraction ) on the other. If light is to move from the water into the air, it will be refracted twice: once at the water/plastic interface and once at the plastic/air interface.

A) If the light strikes the plastic (from the water) at an angle theta w, at what angle Theta a, does it emerge from the plastic (into the air)?
Express your answer in terms of Nw, Np,Na ,Theta w and . Remember that the inverse sine of a number x should be entered as asin(x) in the answer box.

B)What is the distance to the object in terms of Theta w and L?
Express your answer in terms of Theta w and L.

Explanation / Answer

There are two important angles within the plastic: the angle immediately after the first refraction (the water/plastic interface) and the angle immediately before the second refraction (the plastic/air interface). To find out how they relate, draw a picture with the path the light follows in the plastic and the normals to both surfaces. Once you have labeled both angles, keep in mind that the surfaces are parallel, and thus their normals are parallel lines. An important theorem from geometry will give you the relationship between the angles. If two parallel lines are cut by a transversal (a third line not parallel to the first two), then alternate interior angles are congruent. b) D = l/ tan (theta w )

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