A concave mirror of focal length 10cm and a convex mirror of focal length 15cm are placed facing each other 40cm apart. A point object is placed between the mirrors, on their common axis and 15cm from the concave mirror. Find the position and nature of the image produced by successive reflections, first at the concave mirror and then at the convex mirror.

Answer

13

Explanation

Let the situation be as shown in figure with the object and iamge shown at `A` . For image farmation by concave mirror,
`u=-x`
`f=-f`
`(1)/(v)=(1)/(f)-(1)/(u)=-(1)/(f)+(1)/(x) rArr v=(fx)/(f-x)`
`therefore` Distance of the image from the convex mirror `=4f+(fx)/(f-x)=(4f^(2)-3fx)/((f-x))`
`u=-((4f^(2)-3fx))/((f-x))`
`f=f`
By the question,
`v=-(4f-x)` `therefore` `(1)/(v)=(1)/(f)-(1)/(u) gives` ,
`(1)/(-(4f-x))=(1)/(f)+((f-x))/((4f^(2)-3fx))`
on solving, we get,
`x^(2)-6fx+6f^(2)=0`
which gives, `x=(3+-sqrt3)f` But `xlt4f`
Hence, `x=(3-sqrt3)10 cm=12.68 cm`