Q 1 :    

A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is               [2024]

  • -15 cm

     

  • 45 cm

     

  • -45 cm

     

  • 15 cm

     

     

(A)        Given R = 30 cm

              f=R2=+15cm

             Magnification (m) = ±1/2

             For convex mirror, virtual image is formed for real object, therefore, m is +ve

             The mirror formula,

              1v+1u=1fv=ufu-f

              Magnification, m=-vu=-ufu(u-f)=ff-u

             12=ff-u=1515-uu=-15cm



Q 2 :    

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be             [2024]

  • 10/3 cm

     

  • -20 cm

     

  • -10 cm

     

  • 15 cm

     

(3)

Magnification, m=2=-vu

2=-(15-u)-u

2u=15-u

3u=15u=5 cm

1f=1v+1u=110+1-5=1-210=-110

f=-10 cm