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 ×[tex]\frac{\lambda D }{d}[/tex] ...............1
and we have given 10th bright fringe overlap = 9th bright fringe of 600 nm
so here
10 × [tex]\frac{\lambda D }{d}[/tex] = 9 × 600 × [tex]\frac{D}{d}[/tex]
solve it we get [tex]\lambda[/tex]
[tex]\lambda[/tex] = 9 × [tex]\frac{600}{10}[/tex]
[tex]\lambda[/tex] = 540 nm
so unknown wavelength is 540 nm
The unknown wavelength is equal to 540 nanometers.
Given the following data:
To determine the unknown wavelength:
At the maximum distance, the nth bright fringe is given by the formula:
[tex]Y = \frac{n\lambda D}{d}[/tex]
From the question, we were told that the 10th bright fringe of the unknown wavelength overlaps the 9th bright fringe of the 600 nm light.
Mathematically, this can be expressed as follows:
[tex]Y_{10} = Y_9\\\\\frac{10WD}{d} =\frac{9\times 600D}{d} \\\\10W=5400\\\\W=\frac{5400}{10}[/tex]
W = 540 nanometers.
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