1.

Consider a transparent hemisphere (n=2) in front of which a small object is placed in air (n=1) as shown. Consider a ray starting from O which strikes the spherical surface at grazing incidence (i=90^(@)) Taking x=R what will be the angle (from the normal) at which the ray emerges from the plane surface.

Answer»

`90^(@)`
`0^(@)`
`30^(@)`
`60^(@)`

Solution :`(1) mu_(2)/V-mu_(1)/u=(mu_(2)-mu_(1))/R`
Taking refraction first at curve surface
`2/v_(1)+1/x=1/R Rightarrow v_(1)=(2Rx)/(x-R)`
for PLANE surface
`v'=v_(1)-R Rightarrowv'=(xR+R^(2))/(x-R)Rightarrow1/v-(2(x-R))/(R(x+R))=0`
`1/v=(2(x-R))/(R(x+R))`
for virtual image
`1/vlt0 Rightarrow(2(x-R))/(R(x+R))lt0`
`xltR`
(2)For`x=2R`
`v_(1)=(4R^(2))/R=4R Rightarrow u=-2R`
`m_(1)=mu_(1)/mu_(2).v/u=1/2. (4R)/((-2R))=-1`
`m_(2)=1 Rightarrow m_(1)m_(2)=-1` Image is REAL inverted and same size.


Discussion

No Comment Found

Related InterviewSolutions