A screen is separated from a double-slit source by 1.20 m. The distance between

Question

A screen is separated from a double-slit source by 1.20 m. The distance between the two slits is 0.0300 mm. The second-order bright fringe (m = 2) is measured to be 4.50 cm from the centerline. Determine (a) the wavelength of the light and (b) the distance between adjacent bright fringes.

SOLUTION

(A) Determine the wavelength of the light.

(B) Determine the distance between adjacent bright fringes.

Use the bright fringe equation again to find the distance between any adjacent bright fringes (here, those characterized by m and m + 1).

PRACTICE IT

Use the worked example above to help you solve this problem. A screen is separated from a double-slit source by 1.28 m. The distance between the two slits is 0.0308 mm. The second-order bright fringe (m= 2) is measured to be 4.30 cm from the centerline.

Suppose the same experiment is run with a different light source. If the first-order maximum is found at 2.00 cm from the centerline, what is the wavelength of the light?

Explanation / Answer

a) for mth order nright fringe,

y = m * lambda * D / d

for m = 2 ,

4.30 x 10^-2 = 2 x lambda x 1.28 / (0.0308 x 10^-3)

lambda = 517 x 10^-9 m = 517 nm

b) when m = 1

then y will be 4.30/2 = 2.15 m

distance = 4.30 - 2.15 = 2.15 m

------------------------------------

now, 2 x 10^-2 = 1 * lambda * 1.28 / (0.0308 x 10^-3)

llambda = 481 x 10^-9 m = 481 nm

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