PHYS 1610
Exam 4 - Take Home
Merrill
6. [15 pts.] A beam of light is incident from air \( \left(n_{\text {air }}=1\right) \) onto oil \( \left(n_{\text {oil }}=1.45\right) \) floating on water \( \left(n_{\text {water }}=1.33\right) \). The angle of incidence \( \theta_{a} \) of the beam onto the oil is \( 30^{\circ} \). The oil has a thickness of \( 1.20 \mu \mathrm{~m} \).
(A). Find the angle of refraction \( \theta_{o} \) of the beam in the oil.
(B). Find the separation \( x \) between the point where the beam enters the water from the oil and the point where the beam would enter the water if the oil weren't there. (See the picture.)
(C). For \( 660-\mathrm{nm} \) light, the index of refraction of water is 1.331 . For \( 410-\mathrm{nm} \) light, the index of refraction of water is 1.342 . Find the difference in the angle of refraction in the water \( \Delta \theta_{w} \) between \( 660-\mathrm{nm} \) light and \( 410-\mathrm{nm} \) light.
Visual Representation: Sketch a simple picture of what is happening, important quantities involved, and what you are solving for. Draw a free-body diagram, if appropriate. (This step has partly been completed for you.)
[2 pt.] Relevant concepts: Any physics concepts needed to answer the questions.
[2 pt.] Information needed: List relevant known quantities or values given. List relevant unknown quantities you will need to find out.
[10 pt.] Solution: Use the space below and on the next page to answer the questions. Work calculations out algebraically (using letters) and plug in numbers as the last step.
