Deviation without dispersion and disperison without deviation What should be the condition on a combination of prism for the following ? (a) Angle of dispersion is zero but angle of deviation is not zero.

Deviation without dispersion and disperison without deviation What sh

1.	Deviation without dispersion and disperison without deviation What should be the condition on a combination of prism for the following ? (a) Angle of dispersion is zero but angle of deviation is not zero.
Answer» Solution :(1) Deviation without DISPERSION is not possible for a single prism but we can combine two or more prisms so that dispersion is zero. Such a COMBINATION is known as achromatic combination of prisms. `delta_(1)+delta_(2) ne 0`, but in this case `theta_(1)+theta_(2)=0` Calculation We have `(n_(v_(1))-n_(R_(1)))A_(1)+(n_(V_(2))-n_(R_(2)))A_(2)=0` Since `n_(V)-n_(R )` is always greater than `0`, this is possible only where `A_(1)` and `A_(2)` are of the opposite signs. That is, `A_(2)=-((n_(V_(1))-n_(R_(1)))/(n_(V_(2))-n_(R_(2))))A_(1)` Now, `delta=delta_(1)+delta_(2)` `=(n_(V_(1))-1)A_(1)+(n_(v_(2))-1)A_(2)` `=(n_(V_(1))-1)A_(1)-(n_(V_(2))-1)((n_(V_(1))-n_(R_(1)))/(n_(V_(2))-n_(R _(2))))A_(1)` `=(n_(V_(1))-1)A_(1)[1-((n_(V_(1))-n_(R_(1)))/(n_(V_(1))-1)))((n_(V_(1))-1)/(n_(V_(2))-n_(R_(2))))]` `=delta_(1)[1-(omega_(1))/(omega_(2))]` (b) ANGLE of deviation is zero but angle of dispersion is not zero. (1) Dispersion without deviation is not possible for a single prism but we can combine two or more prisms so that deviation is zero. Such a combination is known as direct vision prism. (2) Mathematically we want that `delta_(1)+delta_(2)=0` but in this case `theta_(1)+theta_(2) ne 0` Calculation we know that `delta=delta_(1)+delta_(2)=0` where `delta` is average deviation for each prism , that is `(n_(V_(1))-1)A_(1)+(n_(V_(1))-1)A_(2)=0` `A_(2)=-(n_(Y_(1))-1)A_(1))/((n_(y_(1))-1))` This would mean that in this case also both angles of the prism are of opposite signs. `theta=theta_(1)+theta_(2)` Now, `theta_(1)=(n_(v_(1))-n_(R_(1))A_(1)` `theta_(2)=(n_(v_(2))-n_(R_(2))A_(2)` `theta=(n_(V_(1))-n_(R_(1)))A_(1)-(n_(V_(2))-n_(R_(2)))((n_(V_(1))-1)A_(1))/((n_(V_(2))-1))` Substituting the value of `A_(2)`, we get `(n_(V_(1))-n_(R_(1)))[1-[((n_(V_(2))-n_(R_(2)))/(n_(Y_(1))-1))((n_(Y_(2))-1)/(n_(V_(1))-n_(R_(2))))]]` Finally, we have `theta=theta_(1)+theta_(2)=theta_(1)[1-(omega_(2))/(omega_(1))]` (Only yellow color ray will not deviate, all other colored rays will deviate Learn : This kind of combination of prisms is possible only if the prisms are kept INVERTED with respect to each other as shown in the Fig. 34-67.

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Deviation without dispersion and disperison without deviation What should be the condition on a combination of prism for the following ? (a) Angle of dispersion is zero but angle of deviation is not zero.

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