Question

# A graph is plotted between the angle of deviation $\delta$ and angle of incidence $i$ for a prism. The nearly correct graph is

Open in App
Solution

## The graph between the angle of deviation and angle of incidence:Explanation:From the relation of the angle of incidence to the angle of deflection:$\delta =i-A+{\mathrm{sin}}^{-1}\left(n·\mathrm{sin}\left(A-{\mathrm{sin}}^{-1}\left(\frac{\mathrm{sin}i}{n}\right)\right)\right)$Here,$i=Angleofincidence\phantom{\rule{0ex}{0ex}}\delta =Angleofdeflection\phantom{\rule{0ex}{0ex}}A=Angleofprism\phantom{\rule{0ex}{0ex}}n=refractiveindex$When we plot the graph of the above relation it comes out to be of parabolic nature with a minimum.The minimum value of angle of deviation $\delta$ is at the point where $i=e$ i.e. angle of incidence is equal to the angle of emergence.In the given graph as the value of the angle of incidence $i$ increases the value of the angle of deviation $\delta$ decreases nonlinearly until it reaches its minimum value at $i=e$ and then the value of $\delta$ starts increasing and hence form a downward parabola.Hence, the graph between angle of incidence and angle of deviation is a parabola with minimum deviation at $i=e$.

Suggest Corrections
0