I need help answering this physics question involving slits and wavelength. A li

Question

I need help answering this physics question involving slits and wavelength.

A light beam shines through a thin slit and illuminates a distant screen. The central bright fringe on the screen is 1.00 cm wide, as measured between the dark fringes that border it on either side. Decreasing the wavelength of the light would decrease the width of the central bright fringe. Decreasing the width of the slit would decrease the width of the central bright fringe. A diffraction grating with 10,000 openings/cm is used to determine the wavelength of light from a laser. If the 1st-order bright fringe is 50.0 cm from the center of the viewing screen, and the viewing screen is 86.6 cm from the diffraction grating, then what is the wavelength? Assume the diffraction grating and screen are parallel. Light of wavelength 415 nm passes through the diffraction grating described in the previous problem and makes an interference pattern on the viewing screen described in the previous problem. How many bright fringes appear on the viewing screen? Assume the diffraction grating and screen are again 86.6 cm apart and parallel. In a double-slit experiment, the slits are 2.00 mm apart. A mixture of two wavelengths of light shines on the slits and this light is diffracted though the slits. The wavelengths are lambda 1 = 750.0 nm and lambda 2 = 900.0 nm. The two interference patterns share a common central maximum. On a screen positioned 2.00 m from the slits, at what minimum distance from the central maximum will a bright fringe of one wavelength light coincide (overlap exactly) with a bright fringe of the other wavelength light? Two sources of light illuminate a double slit simultaneously. One has wavelength 630 nm and the second has an unknown wavelength. The m = 5 bright fringe of the unknown wavelength overlaps the m = 4 bright fringe of the light of 630 nm wavelength. What is the unknown wavelength?

Explanation / Answer

apply Y = mLR/d

where Y = fringe width

L = waelength

R = distance dfrom slit to scrren

d = slit width

1.a. as L is directly propotational Y,

and Y is inerlsy poroportiinal to d,

i is true and ii is flase

2. L = Yd/mR

L = (1/1000)*10^-2 * 0.5/(1* 0.866)

L =5.77 um

3. m = 5.77/415 = 14 fringes

4. Y2-Y1 = 1*(900-750)nm * 2/(2*10^-3)

DY = 0.15 mm

5. y5 = 5* 630nm *R/d

Y4 = 4* L2*R/d

since Y4 = Y5

L2 = 5*630/4

L2 = 787.5 nm

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