Question 143: Wave Optics

Question

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength $$\lambda $$ such that the first minima occurs directly in front of the slit (S
1
) ?

Accepted Answer

Path difference, S
2
P Ã¢ÂÂ S
1
P = $${\lambda  \over 2}$$
$$ \Rightarrow $$ $$\sqrt {4{d^2} + {d^2}}  - 2d = {\lambda  \over 2}$$
$$ \Rightarrow $$ $$d\left( {\sqrt 5  - 2} \right) = {\lambda  \over 2}$$
$$ \Rightarrow $$ d = $${\lambda  \over {2\left( {\sqrt 5  - 2} \right)}}$$

Answer

$${\lambda  \over {2\left( {5 - \sqrt 2 } \right)}}$$

Answer

$${\lambda  \over {2\left( {\sqrt 5  - 2} \right)}}$$

Answer

$${\lambda  \over {\left( {5 - \sqrt 2 } \right)}}$$

Answer

$${\lambda  \over {\left( {\sqrt 5  - 2} \right)}}$$

Wave Optics

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength $\lambda $ such that the first minima occurs directly in front of the slit (S 1 ) ?

Choose the correct answer: