Physics

Problem

A monochromatic source

S_{1}

of wavelength

\lambda_{1}

produces a fringe width

\beta_{1}

in a Young’s double–slit experiment using slit separation

d

and screen distance

D

. In a second trial the source is replaced by another source

S_{2}

of wavelength

\lambda_{2}

; simultaneously the screen is moved so that its distance from the slits becomes

D/2

and the slit separation is changed to

3d

. a. (a) Derive an expression for the new fringe width

\beta_{2}

in terms of

\lambda_{2}

D

and

d

. b. (b) Hence obtain the ratio

\dfrac{\beta_{2}}{\beta_{1}}

. c. (c) Evaluate

\dfrac{\beta_{2}}{\beta_{1}}

when

\lambda_{1}=500\,\text{nm}

and

\lambda_{2}=400\,\text{nm}

. d. (d) State clearly whether the fringes in the second trial are wider or narrower than in the first, supporting your answer with the calculated ratio.

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