Ishaan Booker

2022-07-17

White light is spread out into its spectral components by a diffraction grating. If the grating has 2085 lines per centimeter, at what angle does red light of wavelength 640 nm appear in first-order spectrum?

Jorge Franklin

Beginner2022-07-18Added 11 answers

Given in question: Number of slits(N) = 2085 lines/cm = 208500 lines/m

$\text{Wavelength}(\lambda )=640\text{}nm=640\times {10}^{-9}\text{}m$

Order(n) = 1

To find: Angle($\theta $)

Solution: Step1 - Calculating the grating constant(d).

As we know,

Grating spacing(d) $=1N=1208500=4.8\times {10}^{-6}\text{}m$

Calculating the angle($\theta $).

As we know that, grating condition is given by:

$d\mathrm{sin}(\theta )=n\lambda $

$\theta ={\mathrm{sin}}^{-1}(\frac{n\lambda}{d})={\mathrm{sin}}^{-1}(\frac{1\times 640\times {10}^{-9}}{4.8\times {10}^{-6}})$

$\theta ={\mathrm{sin}}^{-1}(0.1333)={7.66}^{\circ}$

Hence, the angle will be (${7.66}^{\circ}$)

$\text{Wavelength}(\lambda )=640\text{}nm=640\times {10}^{-9}\text{}m$

Order(n) = 1

To find: Angle($\theta $)

Solution: Step1 - Calculating the grating constant(d).

As we know,

Grating spacing(d) $=1N=1208500=4.8\times {10}^{-6}\text{}m$

Calculating the angle($\theta $).

As we know that, grating condition is given by:

$d\mathrm{sin}(\theta )=n\lambda $

$\theta ={\mathrm{sin}}^{-1}(\frac{n\lambda}{d})={\mathrm{sin}}^{-1}(\frac{1\times 640\times {10}^{-9}}{4.8\times {10}^{-6}})$

$\theta ={\mathrm{sin}}^{-1}(0.1333)={7.66}^{\circ}$

Hence, the angle will be (${7.66}^{\circ}$)

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