Laser light is shown through a diffraction grating with a line density of 300 li

Question

Laser light is shown through a diffraction grating with a line density of 300 lines/mm .  The 2nd order maximum is measured to be 2.40 m away from the center on a screen that is 4.12 m from the diffraction grating.  the wavelength of the laser is 839 nm.

a)How many laser dots are visible on the screen (assuming that the wall is large enough)?

b)What is the total distance between the two first order maxima on the wall?

c)If the laser were replaced with a 671 nm laser instead, at what distance from the central maximum would the second order be located?

Explanation / Answer

a)
width of each slit, d = 1/300

= 3.33*10^-3 m

= 3.33*10^-6 m

R = 4.12 m

from the given data the angle for second order maxima, theta = tan^-1(2.4/4.12)

= 30.2 degrees

d*sin(theta) = n*lamda

for maximum n value, theta = 90 degrees

d*sin(90) = n*lamda

==> n = d/lamda

= 3.33*10^-6/(839*10^-9)

= 4

so, we get 2*4 + 1 = 9 laser dots on the screen .

b)
distance between two first order slits = 2*lamda*R/d

= 2*839*10^-9*4.12/(3.33*10^-6)

= 2.08 m

c) y2 = 2.4*671/839

= 1.92 m

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