Question 104: Wave Optics

Question

Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio of 9 : 16. (Assuming intensity of light is directly proportional to the width of slits)

Accepted Answer

Let,
Width of first slit = w
1
and width of second slit = w
2
Given, $${{{w_1}} \over {{w_2}}} = {9 \over {16}}$$
Given,
Intensity of light $$(I) \propto w$$
$$	herefore$$ $${{{I_1}} \over {{I_2}}} = {{{w_1}} \over {{w_2}}} = {9 \over {16}}$$
We know,
$${{{I_{\max }}} \over {{I_{\min }}}} = {\left( {{{\sqrt {{I_1}}  + \sqrt {{I_2}} } \over {\sqrt {{I_1}}  - \sqrt {{I_2}} }}} ight)^2}$$
$$ = {\left( {{{\sqrt {{{{I_1}} \over {{I_2}}}}  + 1} \over {\sqrt {{{{I_1}} \over {{I_2}}}}  - 1}}} ight)^2}$$
$$ = {\left( {{{{3 \over 4} + 1} \over {{3 \over 4} - 1}}} ight)^2}$$
$$ = {\left( {{7 \over 1}} ight)^2}$$
$$ = {{49} \over 1}$$

Answer

3 : 4

Answer

4 : 3

Answer

7 : 1

Answer

49 : 1

Wave Optics

Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio of 9 : 16. (Assuming intensity of light is directly proportional to the width of slits)

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