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Chapter 5: Q37E (page 1213)

Monochromatic light with wavelength 620 nm passes through a circular aperture with diameter 7.4渭m. The resulting diffraction pattern is observed on a screen that is 4.5 m from the aperture. What is the diameter of the Airy disk on the screen?

Short Answer

Expert verified

On the screen, the diameter of the disk is 0.92 m

Step by step solution

01

Given Data

The light鈥檚 wavelength is 620 nm

The aperture鈥檚 diameter is 7.4渭尘

The separation between screen and aperture is 4.5m

02

Rayleigh Criterion

According to the Rayleigh criterion for the limit to resolution, two images are only resolvable when the center of one's diffraction pattern is directly over the first minimum of the other's diffraction pattern.

厂颈苍胃=1.22位d

Hereis the angle of diffraction, 位is the wavelength of light used and dis the diameter of the aperture.

03

Diameter of the airy disk

According to Rayleigh,

蝉颈苍胃=1.22位d=1.22620nm7.4渭尘=1.22620脳109m7.4脳106m=0.102

As,胃 is verysmall

蝉颈苍胃鈮�胃=0.102鈮�迟补苍胃

Now the radius of the disk is

r=R迟补苍胃=(4.5m)脳0.102=0.46m

Therefore, diameter

d=2r=2脳0.46m=0.92m .

Hence, the diameter of the disk is 0.92 m .

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