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  • In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water?

Q10.7  In a double-slit experiment the angular width of a fringe is found to be 0.2° on a screen placed 1 m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be 4/3.

Answers (1)

best_answer

Given

The angular width of the fringe when the medium is air

\theta _{air}=0.2^0

The distance of the screen from the slit  D = 1m

The wavelength of light we are using \lambda=600nm=600*10^{-9}m

Refractive index of water  \mu_{water}=4/3

let angular width of fringe when the medium is water \theta _{water}

Now, as we know the angular width is given by 

\theta =\frac{\lambda }{d}

so,

d=\frac{\lambda _{air}}{\theta _{air}}=\frac{\lambda _{water}}{\theta _{water}}

d=\frac{\lambda _{air}}{\lambda _{water}}=\frac{\theta _{air}}{\theta _{water}}=\mu

 

From here 

\theta _{water}=\frac{\theta _{air}}{\mu _{water}}=\frac{3}{4}0.2^0=0.15^0

Hence angular width of the fringe in the water is 0.15^0.

 

Posted by

Pankaj Sanodiya

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