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### Apparent Thickness Formula

Apparent Thickness Formula: n/u = n’/u’

Where:

n = index of refraction for where the light is coming from

n’ = index of refraction for where the light is going to

u = object distance

u’ = image distance

**Question: **A butterfly is embedded 10cm deep in a piece of CR-39 (n = 1.498) lens material. How far into the lens material does the butterfly appear to be?

**Answer: **Using the formula n/u = n’/u’, 1.498/10cm = 1/u’, u’ = 10cm/1.498 = 6.68cm.

**NOTE: Light leaves the object of regard, not the eye. In this case, although we are looking into the block of plastic at the butterfly, light is coming from the butterfly. For this reason, n = 1.498.

**Question: **If a fisherman is going to spear a fish that is 50cm below the surface of the water, which he sees at an angle of 40° from the surface of the water, where should he aim to spear the fish? (Figure 17)

**Answer: **The image that is viewed, as 40° from the surface of the water will be 50° from the normal (a line perpendicular with the surface of the water). Using the formula n sin i = n’ sin r; 1.33 sin r = 1 sin 50°; r = 35.17°.

Using the formula n/u = n’/u’ = 1/u’ = 1.33/50cm, u’ = 50cm/1.33 = 37.59cm.

Therefore, the fisherman should aim behind and below the fish because light from the fish is passing from a more dense to a less dense medium and will be refracted away from the normal. The fisherman sees a virtual image ahead of and above the actual fish.

Click on image to enlarge.

**Reflection and refraction of smooth surfaces**

When light enters a medium, it may be: reflected off the surface, refracted (bending of light due to a change in velocity when it hits the medium) or absorbed (where it is changed into a different type of energy).

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