Does the spacing between fringes in a two-slit interference pattern increase, de

Question

Does the spacing between fringes in a two-slit interference pattern increase, decreased, or stay the stay the same under each of the conditions? (You need to explain your answer for full credit!) (a) If the slit separation is increased. (b) If the color of the light is switched from red to blue (c) If the whole apparatus submerged in generic beer (assume that index of refraction of generic beer is pretty much close to water, or n almostequalto 1.33) (d) What happens to the interference pattern if you close one of the slits completely? (e) What to the interference pattern if you shine blue light through one slit, and red through the other?

Explanation / Answer

We know that spacing between the fringes is given by

y = m lambda D/d

where, y is the spacing, m is the order, lambda is the wavelength, D is the distance of the screen and d is the slit width.

a)If the slit separation is increased, y decreases as it is inversely proportional to d

b)lambda-red = 650 nm and lambda-blue = 475 nm

So the wavelength is decreasing, y is directly proportional to lambda and y will also decrease.

c)walelength in a medium is given by

lambda = lambda(air)/n

so it decreases by a factor of 1/n, and since y is directly proportional to lambda, it will also decrease.

d)The interference pattern will disappear, as minimum of two coherent light sources are required.

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