A student holds a laser that emits light of wavelength λ. The laser beam passes though a pair of slits separated by a distance d, in a glass plate attached to the front of the laser.

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A student holds a laser that emits light of wavelength λ. The laser beam passes though a pair of slits separated by a distance d, in a glass plate attached to the front of the laser. The beam then falls perpendicularly on a screen, creating an interference pattern on it. The student begins to walk directly toward the screen at speed v. The central maximum on the screen is stationary. Find the speed of the mth-order maxima on the screen, where m can be very large. (Use any variable or symbol stated above as necessary.)
vmth-order =

asked Apr 14, 2012 in Physics by Gummmys ~Expert~ (1,105 points)
    

1 Answer

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Best answer

This question can be solved using Young's double slit method.

Which states that:

d*sin(theta) = m*λ

however, since the question states that may be very large we are unable to use small angle approximation for theta.

So instead you must use tangent of the angle to solve for y, which is the spped of the distance between mth-order maxima on the screen.

tan(theta) = y/L       (*where y=distance between mth-order maxima, L=horizontal length)

rearranging this you can solve for y:

y = L*tan(theta)

theta can be solved through the first equation for young's double slit method:

d*sin(theta) = m*λ

theta = inverse sin(m*λ / d)

so plugging theta back in the equation for y we get:

y = L*tan(inverse sin(m*λ / d))

since we are looking for the velocity of the mth order maxima, we must take the derivitative of this equation with respect to time.

As a result of this dL/dt  is equal to v. 

So the final answer is:

 

answered Apr 21, 2012 by kirby ~Expert~ (3,020 points)
selected Apr 21, 2012 by Gummmys

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