If the distance between two slits is 0.75 pin and the distance to a screen is 1.

Question

If the distance between two slits is 0.75 pin and the distance to a screen is 1.5 m, find the angular spacing between the first-order bright fringes for light of 579 nm and 632 nm wavelength. Two planets are circling a star 25.1 light years away and can just be resolved by a 60 cm diameter telescope which is equipped with a filter that only allows light of wavelength 600 nm to pass. What is the distance between the two planets? (1 light year = 9.5 x 10^15 m) Sunlight is reflected from the smooth surface of a pond of water. What is the sun's angle above the horizon when the polarization of the reflected light is the greatest? What is the polarizing angle for light in water hitting a diamond (n=2.39)? Suppose a glass (n=1.45) converging lens with a given focal length is placed in a liquid (n=1.36). What will happen to the focal length of the lens (i.e. increase, decrease, or remain unchanged)? Explain.

Explanation / Answer

The first order bright fringe for 579 nm light is found at,

y1 = D1/d = (1.5 m)(579 nm)/[0.75X10-6m] = 1.5 m(579/750)

or, y1 = 1.158 m

tan1 = y1/D = 1.158 m/1.5 m

or, 1 = 37.660

first order bright fringe for 632 nm light is found at

y2 = D2/d = (1.5 m)(632 X10-9)/[0.75X10-6m] = 1.264 m

tan2 = y2/D = 1.264 m/1.5 m

or, 2 = 40.120

So angular sspacingn is,

=  2 -  1 = 40.120 - 37.660

or, = 2.450 is the angular spacing between first order bright fringes of the two lights.

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