Answer:
The wavelengths are
[tex]\lambda_1 = 614\ nm [/tex]
[tex]\lambda_2 = 687\ nm [/tex]
[tex]\lambda_3 = 975\ nm [/tex]
Explanation:
From the question we are told that
The number of slits per mm is N = 1200
The distance of the screen is [tex]D = 79.0 \ cm = 0.79 \ m[/tex]
The first distance where First-order maxima is observed is [tex]y_1 = 58.2 cm = 0.582 \ m [/tex]
The second distance where First-order maxima is observed is [tex]y_2 = 65.2 \ cm = 0.652 \ m [/tex]
The second distance where First-order maxima is observed is [tex]y_2 = 92.5 \ cm = 0.925 \ m [/tex]
Generally the distance of separation between the slits is mathematically represented as
[tex]d = \frac{1}{1200}= 8.33 *10^{-4} \ mm = 8.33 *10^{-7} \ m[/tex]
Considering the first distance where First-order maxima is observed
Generally the the first distance where First-order maxima is observed is mathematically represented as
[tex]y_1 = \frac{\lambda_1 * D}{d}[/tex]
=> [tex]\lambda_1 = \frac{0.582 * 8.33 *10^{-7} }{0.79}[/tex]
=> [tex]\lambda_1 = 6.14 *10^{-7} m [/tex]
=> [tex]\lambda_1 = 614\ nm [/tex]
Considering the second distance where First-order maxima is observed
Generally the the second distance where First-order maxima is observed is mathematically represented as
[tex]y_2 = \frac{\lambda_2 * D}{d}[/tex]
=> [tex]\lambda_2 = \frac{0.652 * 8.33 *10^{-7} }{0.79}[/tex]
=> [tex]\lambda_2 = 6.87 *10^{-7} m [/tex]
=> [tex]\lambda_2 = 687\ nm [/tex]
Considering the third distance where First-order maxima is observed
Generally the the third distance where First-order maxima is observed is mathematically represented as
[tex]y_3 = \frac{\lambda_3 * D}{d}[/tex]
=> [tex]\lambda_3 = \frac{0.925 * 8.33 *10^{-7} }{0.79}[/tex]
=> [tex]\lambda_3 = 9.75 *10^{-7} m [/tex]
=> [tex]\lambda_3 = 975\ nm [/tex]
