Question

Light illuminating a pair of slits contains two wavelengths, 600 nm and an unknown wavelength. The 10th bright fringe of the unknown wavelength overlaps the 9th bright fringe of the 600 nm light.
1. What is the unknown wavelength?

Answer 1

Answer:

unknown wavelength is 540 nm

Explanation:

given data

wavelengths =  600 nm

10th bright fringe overlap = 9th bright fringe of 600 nm

to find out

unknown wavelength

solution

we get  here first nth bright fringe from the central maximum at distance y

y = n ×$\frac{\lambda D }{d}$   ...............1

and we have given 10th bright fringe overlap = 9th bright fringe of 600 nm

so here

10 × $\frac{\lambda D }{d}$ = 9 × 600 × $\frac{D}{d}$    

solve it we get $\lambda$

$\lambda$ = 9 × $\frac{600}{10}$

$\lambda$ = 540 nm

so unknown wavelength is 540 nm