Answer:
[tex]\theta_1 = 0.400^o[/tex]
[tex]\theta_2 =0.378^o[/tex]
Explanation:
From the question we are told that
The number of slits per cm is k = [tex]161\ slits\ per\ cm = 161 \ slits\ per\ 0.01 m[/tex]
The order of the maxima is n = 1
The wavelength are [tex]\lambda_1 = 434 nm = 434 *10^{-9} \ m \ \ \ , \lambda_2 = 410nm = 410 *10^{-9} \ m[/tex]
The spacing between the slit is mathematically represented as
[tex]d = \frac{ 0.01}{k}[/tex]
=> [tex]d = \frac{ 0.01}{161}[/tex]
=> [tex]d = 6.211 *10^{-5} \ m[/tex]
Generally the condition for constructive interference is
[tex]n\lambda = d \ sin \theta[/tex]
At [tex]\lambda_1[/tex]
[tex]\theta _1 = sin^{-1} [ \frac{1 * 434 *10^{-9}}{6.211 *10^{-5}} ][/tex]
[tex]\theta_1 = 0.400^o[/tex]
At [tex]\lambda_2[/tex]
[tex]\theta _2 = sin^{-1} [ \frac{1 * 410 *10^{-9}}{6.211 *10^{-5}} ][/tex]
[tex]\theta_2 =0.378^o[/tex]
