A convex lens of radii of curvature 20cm and 30 cm respectively. It is silvered at the surface which has smaller radius of curvature. Then it will beh
A convex lens of radii of curvature 20cm and 30 cm respectively. It is silvered at the surface which has smaller radius of curvature. Then it will behave as `(mu_(g) = 1.5)`
A. concave mirror with equivalent focal length `30/11 cm`.
B. concave mirror with equivalent focal length `60/11 cm`.
C. convex mirror with equivalent focal length `30/11 cm`.
D. convex mirror with equivalent focal length `60/11 cm`.
1 Answers
Correct Answer - B
Focal length for lens, `1/(f_(L)) = (mu_(g) - 1) (1/(R_(1)) - (1)/(R_(2)))`
Here `mu_(g) = 1.5, R_(1) = 20 cm, R_(2) = -30 cm`
`:. (1)/(f_(L)) = (1.5-1) (1/20-1/(-30)) = 0.5 xx (5/60)`
or `d_(L) = 120/5= 24 cm`
Focal length for mirror, `f_(m) = r/2 = (-20)/(2) = - 10 cm`
`:.` Equivalent focal length
`f_(eq) = (-2)/(f_(L)) + (1)/(f_(m)) = (-2)/(24) + (1)/(-10) = (-11)/(60) rArr f_(eq) = (-60)/(11) cm`
Hence, this system behaves like a concave mirror of focal length `(-60)/(11) cm`.