If you send a laser beam through two very narrow slits to a distance screen as i
ID: 2077641 • Letter: I
Question
If you send a laser beam through two very narrow slits to a distance screen as in the figure at the right, you get a pattern of bright bands. In the graphs below are shown the intensity of the light from a variety of different arrangements of the slit widths (d), their separation (a), and the beam's wavelength (lambda). 4.1 Which pair(s) of graphs could represent situations with the same wavelength (lambda), and the same width slits (d), but that are separated by different distances (a)? 4.2 Which pair (s) of graphs could represent situations with the same wavelength (lambda), and the same separation of the slits (a), but that have slits of different widths (d)? 4 3 Which pair(s) of graphs could represent situations with the same width slits (d), and that are separated by the same distances (a), but that are illuminated by different wavelengths (lambda)? 4.4 For situation A, using only the information in the graph, can you determine the ratio of the separation of the slits to the width of the slits, a/d? (Y or N) 4.5 If your answer to 4.4 was Y, find the ratio. If your answer was N, State what additional information you would need to determine that ratio.Explanation / Answer
We have seen that that the interference maxima occur when a sin() = m. On the other hand, the condition for the first diffraction minima is d sin() = . Thus, a particular interference maximum with order m may coincide with the first diffraction minimum. The value of m can be calculated as
a sin()/dsin() = m/ => m=a/d
where a is the separation of slits and d is the width of the slit.
4.1) In this case, every parameter is constant except a. Hence the value of m will be different, but will have the same location for the minima. Graph A and D represent this situation.
4.2) In this case, every parameter is constant except d. Hence the value of m will be same and also different location for the minima. Graph B and E represent this situation.
4.3) In this case, every parameter is constant except .In this situation, there will be same number of fringes, but their location will be different. Graph C and F represent this situation.
4.4) Yes, we can determine the ratio a/d. From the graph, we can easily obtain the number of fringes in the envelop and total length of the envelope.
4.5) It has already been calculated at the top.
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