Question

The two most prominent wavelengths in the light emitted by a hydrogen discharge lamp are 656(red) and 486 (blue). Light from a hydrogen lamp illuminates a diffraction grating with 500 lines per mm, and the light is observed on a screen 1.50 behind the grating. What is the distance between the first-order red and blue fringes?

Answer 1

Answer:

0.145 m

Explanation:

Data provided in the question:

wavelength of red light, λred = 656 nm = 656 × 10⁻⁹ m

wavelength of blue light, λblue = 486 nm = 486 × 10⁻⁹ m

line density = 500 per mm

length, L = 1.3 m

d = 1 mm / 500 lines

= 0.002 mm  = 0.002 × 10⁻⁶ m

m = 1      [for the first order bright fringe]

Now,

The positions can be determined by using the formula

θ = $\sin^{-1}(\frac{m\lambda}{d})$

& y = Ltan(θ)

thus,

θred = $\sin^{-1}(\frac{1\times656\times10^{-9}}{0.002\times{10^{-6}}})$

=  19.15°

yred = Ltan(θred)

= (1.5) × tan(19.15°)

= 0.521 m

similarly,

θblue = $\sin^{-1}(\frac{1\times486\times10^{-9}}{0.002\times{10^{-6}}})$

= 14.1°

yblue = Ltan(θblue)

= 1.3 × tan(14.1°)

= 0.376 m

Hence,

distance between the first-order red and blue fringes

=  0.521 m  - 0.376 m

= 0.145 m