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In the figure shown M(1) and M(2) are tw...

In the figure shown `M_(1)` and `M_(2)` are two spherical mirrors of focal length `20 cm` each. `AB` and `CD` are their principal axes respectively which are separated by `1 cm. PQ` is an object of height `2 cm` and kept at distance `20 cm` from `M_(1)`. The separation between the mirrors is `50 cm` Consider two successive reflections first on `M_(1)` then on `M_(2)`. Find the size of the `2^(nd)` image. Also find distances of and points `P''` and `Q''` of that image from the line `AB`.
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Text Solution

Verified by Experts

The correct Answer is:
distance of p'' from AB = 1 cm .,
distance of Q'' from AB = 7 cm.,

for `M_(1):rarr u=-3-,f=-2-`
`:. (1)/(v)+(1)/(-30)=(1)/(-20)`
`rArr v= -60 cm`
`m_(1)=-(v)/(u)=-(-60)/(-30)=-2`
The image By `M_(1)` is `P'Q'`
for `M_(2) : u =+ 10,f + 20`
`:. (1)/(v)+(1)/(10)=(1)/(-20)`
`rArr v=-20 cm`
`m_(2)=-(-20)/(10)=+2`
now the size of final image is `= 8 cm`.
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