Obtain the condition for maxima and minima of the light reflected from a thin transparent film of uniform thickness. Why is the visibility of the fringe much higher in the reflected system than in the transmitted system.

#### Solution

**i**. The two rays will interfere consecutively if the path difference between them is an integral multiple of λ i.e.

2μt cos r + `λ/2 `= nλ

Or

2μt cos r = (2n-1)`λ/2`

Where,

n= 1, 2, 3, 4, ……….. (for maxima)

or

2μt cos r = (2n-1)`λ/2`

Where n = 0, 1, 2, 3, 4, ………………….

When this condition is satisfied the film will appear bright in the reflected system.**ii.** The two rays will interfere destructively if the path difference between them is an odd multiple of `λ/2` i.e.

2μt cos r +` λ/2 = (2n-1)λ/2`

Or

2μt cos r = nλ (for minima)**iii.** The film which appears bright in reflected light appears dark in transmitted light and vice versa.**iv.** For the transmitted light, the intensity of maxima is about 100% and the minima is about 85%. The result in poor contrast between bright and dark

where in poor contrast between where as in reflected light, minima is having its intensity zero and maxima is nearly 15% of incident energy. This result in good contrast.**v.** Hence visibility of fringe is much higher in reflected system.