1) For your diffraction grating experiment, you need to calculate the wavelength

Question

1) For your diffraction grating experiment, you need to calculate the wavelength of light. Derive the expression for calculating the wavelength () in terms of y1bright. Given the ratio of d to D is 1:1000 and also the angle 1 is 4°.

Wavelength (): ________ *y1bright

2) A laser beam of unknown wavelength shines through the two slits and produces a diffraction pattern with dark bands at y1 = 7.8 mm, y2 = 23.3 mm, and y3 = 38.8 mm from the center of the central intensity maximum. If the distance between the slits d = 70 µm, and the distance between the slits and the screen is D = 174 cm, what is the wavelength of the laser light used?

Incorrect: ________ nm

Explanation / Answer

a)

first dark fringe:

sin1 = /d = y1dark/D >>> = y1dark *d/D = (1/1000)y1dark

second dark fringe:

sin1 = 2/d = y2dark/D >>> = 0.5* y2dark *d/D = (1/2000)y2dark

we know that y1bright = (y2dark + y1dark)/2

>>>> = (1/1500) y1bright

b)

y1bright = (y1dark + y2dark)/2 = 15.55 mm

= y1bright * a/D = 15.55*70/1.74 = 626 nm

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