Violet light (wavelength 400 nm) is incident from the left side of a soap film (
ID: 1322257 • Letter: V
Question
Violet light (wavelength 400 nm) is incident from the left side of a soap film (n = 4/3) as shown in Figure 3 (left). This figure shows the incident ray and several rays that result from the reflection and transmission at the first (left) and second (right) boundaries. The ray that results from the reflection at the second (right) boundary is not shown.
You can assume that light is incident from the left at almost normal incidencethis allows you to ignore any bending of the rays due to Snells law.
a) What are the three minimum thicknesses for which the reflected violet light (rays coming back out on the left side) will interfere:
(i) constructively?
(ii) destructively
b) For the two rays that pass through the second boundary and into air, i.e., the rays coming out on the right side of the film, what are the three smallest film thicknesses for which these rays would interfere:
(i) constructively?
(ii) destructively?
c) How, if at all, would the pattern seen from the
right side of the film differ from the pattern seen from the left side of the film when the thickness of the soap fi lm varies as shown in the side view (Figure 3, right) of the soap film?
d) In this example, what color(s) of light do you see in regions where light interferes constructively?
Violet light (wavelength 400 nm) is incident from the left side of a soap film (n = 4/3) as shown in Figure 3 (left). This figure shows the incident ray and several rays that result from the reflection and transmission at the first (left) and second (right) boundaries. The ray that results from the reflection at the second (right) boundary is not shown. You can assume that light is incident from the left at almost normal incidence?this allows you to ignore any bending of the rays due to Snell?s law. a) What are the three minimum thicknesses for which the reflected violet light (rays coming back out on the left side) will interfere: (i) constructively? (ii) destructively b) For the two rays that pass through the second boundary and into air, i.e., the rays coming out on the right side of the film, what are the three smallest film thicknesses for which these rays would interfere: (i) constructively? (ii) destructively? c) How, if at all, would the pattern seen from the right side of the film differ from the pattern seen from the left side of the film when the thickness of the soap fi lm varies as shown in the side view (Figure 3, right) of the soap film? d) In this example, what color(s) of light do you see in regions where light interferes constructively?Explanation / Answer
a. optical path difference = 2nt+; where t? width of soap film, n?refractive index
1) for constructive interference,
2nt+=
t= 150*10^?9 *(m?1/2) So t= 75nm,225nm, 375nm
2) destructive,
2nt=(m ) ; minimum thickness=150nm ,300nm, 450 nm
b. optical path difference=2nt;
1) for constructive
2nt=(m ); minimum thickness=150nm ,300nm, 450 nm
2) for destructive
2nt=(m+1/2) ; t= 75nm,225nm, 375nm
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