Question

Problem 9: A red laser (λ = 608 nm) is incident on a diffraction grating that has n = 1100 lines per cm. Randomized Variables λ = 608 nm n = 1100 lines/cm  Part (a) What is the angle, in radians, that the first order maximum makes, θ1? Numeric : A numeric value is expected and not an expression. θ1 = __________________________________________ Part (b) What is the angle of the fourth order maximum, θ4, in radians? Numeric : A numeric value is expected and not an expression. θ4 = __________________________________________

Problem 8: Light of wavelength λ = 509 nm passes through a single slit of width w = 3.6 μm and illuminates a screen L = 1.3 m away.

Part (a) How many dark fringes nfringes of light total will this setup produce on the screen? Numeric : A numeric value is expected and not an expression. nfringes = __________________________________________ Part (b) What is the width y, in meters, of the bright central maximum on the screen? Numeric : A numeric value is expected and not an expression. y = __________________________________________

Answer 1

$\lambda$ = 608 nm

n = 1100 lines/cm

For first order , m = 1

e = 1/lines_per_metre = 10^-2/1100 = 9.09 x 10^-6

Sin $\Theta$ = $\lambda$ /e = 608 x 10^-9 / 9.09 x 10^-6 = 66.88 x 10^-3 = 0.06688

$\Theta$ = 0.0669 radians

b.

For fourth order

m = 4

4 $\lambda$ = eSin $\Theta$

Sin $\Theta$ =4 $\lambda$ /e = 4 x 0.06688 = 0.26752

$\Theta$ = 15.5 rad

Problem 8

a. Multiple dark fringes.

b. y = L $\lambda$ /a = 1.3 x 509 x 10^-9 / 3.6 x 10^-6 = 0.183 m