Need help with these questions step by step with a digram if needed. 1. In an ex

Question

Need help with these questions step by step with a digram if needed.

1. In an experiment the first order (m=1) maximums are measured a distance of 8cm apart from scattering due to a diffraction grating placed 70cm away from the screen.

a. If the diffraction grating has 880lines/cm, what is the wavelength of light?

b. If light from this laser is used in a single slit diffraction experiment at what angles would you expect to see minimums appear (please give 3 different positive angles) if the slit width is 10micrometer?

2. In an experiment, the diffraction pattern from a single slit was recorded with light of wavelength 700nm on a screen held 100cm from the slit. The distance between the first order (m=1) minima on either side of the central maximum was measured to be 5.9cm and the corresponding distance for the second order (m=2) was 12.3cm. Calculate the average width of the slit using both the first and second order data.

3. Given the distance between the second order diffraction spots to be 24.0com and the distance between the gratign and the screen to be 110.0cm; calculate the wavelength of the light. The grating had 80 lines/mm.

Explanation / Answer

here,

1)

maximums are measured a distance , y = 8 cm

y = 0.08 m

distance of screen , D = 70 cm

D = 0.7 m

(a)

difference between slits , d = 1/880 cm

d = 1.14 * 10^-5 m

y = D * wavelength /d

0.08 = 0.7 * wavelength / 1.14 * 10^-5

wavelength = 1.3 * 10^-6 m

the wavelength of light is 1.3 * 10^-6 m

(b)

slit width , d = 10 um

d = 10 * 10^-6 m

d*sin(theta) = m * wavelength

10 * 10^-6 * sin(theta) = m * 1.3 * 10^-6

m = 1

10 * 10^-6 * sin(theta1) = 1.3 * 10^-6

theta1 = 7.47 degree

for m = 2

10 * 10^-6 * sin(theta2) = 2 * 1.3 * 10^-6

theta2 = 15.07 degree

for m = 3

10 * 10^-6 * sin(theta3) = 3 * 1.3 * 10^-6

theta3 = 22.95 degree

the three different positive angles are (7.47 , 15.07 and 22.95) degrees

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