6a. 23.6 deg 6b. 44.4 deg 6c. 20.8 deg 7a. .16m 7b. 40m 6. As part of an outreac

Question

6a. 23.6 deg 6b. 44.4 deg 6c. 20.8 deg 7a. .16m 7b. 40m
6. As part of an outreach project, you develop a kit" for grade school students to build their own grating spectroscope. The key element of this is the diffraction grating, which has 1000 grooves per mm. (a) When white light is incident upon the grating, into what angle is first order (m-1) violet light (wavelength 400 nm) diffracted? (b) into what angle is first order (m 1) red light (wavelength-700 nm) diffracted? (c) What is the angular extent needed for the spectroscope? 7. A military spy satellite in orbit 600 km above the Earth's surface has a mirror of diameter 2.5 m. (a) What is the minimum separation of two objects that could be resolved using light of 550 nm? (b) In order to resolve facial features, it must be possible to resolve two objects separated by about 1.0 cm (for example, two eyes). What diameter would the mirror have to be to achieve this resolution while in an orbit of 600 km above the Earth's surface?

Explanation / Answer

As per chegg rules only one question needs to be answered.

6.

Given that,

grating = 1000 / mm = 1/d

d = 0.001 mm = 10-6 m

(a)

m = 1

wavelength lamda = 400 nm

formula for differaction grating,

dsin (thetav) = m lamda

sin (thetav) = 1*400*10-9 / 10-6 = 0.4

thetav =  23.58 deg = 23.6 deg

(b)

if lamda = 700

sin (thetar) = 1*700*10-9 / 10-6 = 0.7

thetar = 44.4 deg

(c)

angular extend = thetar - thetav

angular extend = 44.4 - 23.6 = 20.8 deg

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