Question

24.7.1 Regular problem Light of wavelength 540 nm from a green laser is incident on two slits that are separated by 0.50 mm; the light reaches a square screen 50 cm x 50 cm that is 1 m away from the slits. Describe quantitatively the pattern that you will see on the screen. Show your work, including all four steps of the problem solving method: Sketch and translate • Visualize the situation and sketch it. • Translate givens into physical quantities. Simplify and diagram • Decide if the small-angle approximation is appropriate. • Represent the situation with a ray diagram showing the path of light waves from the two slits to the screen. Represent mathematically • Describe the diagram mathematically. Solve and evaluate • Solve the problem and decide if the answer makes sense.

Answer 1

bright c dore foing Dark fringe I Screen monochromatic light wave from source propagating through forming secondry wavelet enters through the Slits and enterfere on screen produces alternate bright and dark spot called interference pattern Given physical quantities wavelength of light a = 540mm distance between the slits d = 0.50mm Screen dimension =50cm x 50cm distance between Slits and screen D= 1m. 2. As edis can be d <<<D taken' Small angle approximation o is small. rat pe D Screen

take a general boint P where light interfere at a distance from Central powl on screen leaner Draw SQ tsp as o is small Dato il ith difference A is S₂P-sip SP=QP DELTA/Pg No. A =5, P-SIP = dsino y bright finge A must be either zero.ora integral multiple of wavelength (2) For brisnt fringe A = disino = ny d. Yn ins In = NAD - y = * = 5r4px 3 m = os Ist order bright foringes ton" at dist y, from centre, y = AD: 540 x 18 mxlm - 108om extremly large - 0.500 m I which does no) make any sense. For Dark founge A must be Odd multiple d6 17 18 2 (2n+1 1 2 dyn (2n) y - (2n+1) A D 2d ne- y = 31D I 2 7 & 3 x Shox x z 2x0.50x - 8lom . so smale as required This show that d is taot for Interference pattern.