Q.i) How does the angular width of the central maxima in a single slit Fraunhofer diffraction pattern change when the distance between the slit and screen is doubled? ii) In a Fraunhofer diffraction pattern, the first minima of red light (λ = 660 nm) is formed on the first maxima of another light of wavelength λ'. Find the value of λ'.

(i) The central maximum's angular width 2lambda/a is independent of screen distance, so doubling D leaves it unchanged (though the linear width doubles). (ii) Setting the red first minimum onto the first secondary maximum of lambda' gives lambda' = 2lambda(red)/3 = 440 nm.

(i) In single-slit Fraunhofer diffraction the first minima lie at asin(theta) = lambda, so the half-angular width is theta = lambda/a and the full angular width of the central maximum is 2theta = 2lambda/a. This depends only on the wavelength lambda and slit width a - the screen distance D does not appear. Therefore, when D is doubled, the angular width stays the same. (The LINEAR width on the screen, which is about 2lambda*D/a, does double, but the ANGULAR width is unchanged.)

(ii) Positions on the screen:

• First minimum of red light (lambda = 660 nm): a*sin(theta) = lambda, so the position is proportional to lambda.
• First secondary maximum of light lambda': the secondary maxima occur near a*sin(theta) = (n + 1/2)*lambda', so the first one (n = 1) is at (3/2)*lambda'. …