InterviewSolution
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InterviewSolution
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A crown glass prism of angle 5^(@) is to be combined with a flint prism in such a way that the mean ray passes undeviated. Find (a) the angle of the flint glass prism needed and (b) the angular dispersion produced by the combinatino when white light goes through it. Refractive indices for red, yellow, and violet light are 1.541, 1.517 and 1.523, repectively, for crown flass and 1.613, 1.620 and 1.632 for flint glass. |
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Answer» Solution :The deviation produced by the crown prism is `delta=(MU-1)A` and by the flint prism is `delta^(')=(mu^(')-1)A^(')` The prisms are placed with their angles inverted with respect to each other. The deviations are also is OPPOSITE directions. Thus, the net deviation is `delta_(n et)= delta-delta^(')=(mu-1)A-(mu-1)A^(')` (i) a. If the net deviation for the mean ray is ZERO, `(mu-1)A=(mu^(')-1)A^(')` or `A^(')=((mu-1))/((mu^(')-1))A=(1.517-1)/(1.620-1)xx5^(@)` B. The angular dispersion produced by the crown prism is `delta_(V)-delta_(r)=(mu_(v)-mu_(r))A` and that by the flintprism is `delta_(v)^(')-delta_(r)^(')=(mu_(v)^(')-mu_(r)^('))A` The net angulart dispersion is `(delta _(v)-delta_(r))A-(mu_(v)^(')-mu_(r)^('))A` `=(1.523-1.514) xx 5^(@)-(1.632-1.613)xx4.2^(@)` `=-0.0348^(@) ` . The angular dispersion has magnitude `0.0348^(@) `. a. If the net deviation for the mean ray is zero, `(mu-1)A=(mu^(')-1)A^(')` or `A=((mu^(')-1))/((mu^(')-1))A=(1.517-1)/(1.620-1)xx5^@` b. The angular dispersion produced by the crown prism is `delta _(v)-delta _(r)=(mu_(y)-mu_(r))A` and that by the flint prism is `delta_(v)^(')-delta_(r)^(')=(mu_(v)^(')-mu_(r)^('))A` The net angular dispersion is `(mu_(v)-mu_(r))A- (mu_(v)^(')-mu_(r)^('))A` `=(1.523-1.514)xx5^(@)- (1.632-1.613)xx4.2^(@)` `=-0.0348^(@)`. The angular dispersion havs magnitude `0.034^(@)`. |
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