Question

Read para and answer the questions.Ligth is an agent that creates stimulation.Light usually refers to visible light, which is electromagnetic radiation
that is visible to the human eye and is responsible for the sense of sight.
(i)A mirror forms an image which is 30 cm from the object and twice its height
(a)where must mirror be situiated
(b)what is radius of curvature
(c)is it convex or concave
(ii)an object is placed 15 cmfrom (a)converging mirror and (b)a diverging mirror of radius of curvature 20 cm.Calculate image position and magnification in each case

Answer 1

| v - u | = 30 cm  =>  v = u + 30 cm  or  u - 30 cm
magnification = - v/u = 2  or  -2    =>  v = - 2 u  or  2 u
Since m > 1, the mirror is a concave mirror.

there are 4 cases.
1.
    v = u+30 cm  and v = - 2 u
    u = -10 cm  and v = +20 cm  virtual image.
     1/f = 1/v + 1/u  = 1/20 - 1/10 = -1/20
            =>  f  = -20 cm    and R = -40 cm

2)
     v = u + 30 cm    v = 2 u
     u = 30 cm    as u is positive,  this case is not possible.
3)
   v = u - 30 cm  ,  v = - 2 u
       u = +10 cm,          as u > 0, this is not possible.

4)  v = u - 30 cm,  v = 2u
       u = -30 cm        v = -60 cm      => inverted real image
   1/f = -1/60 -1/30 = -1/20    => f = -20 cm ,  R= -40 cm
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a)  concave mirror
     u =  -15 cm    R = -20 cm  f = -10 cm   
           1/v = 1/f - 1/u = -1/10 +1/15 = -1/30         
             v = -30 cm          m = -v/u = -2
 b)  convex mirror
           u = - 15 cm  R = +20 cm   f = +10 cm
       1/v = 1/f - 1/u = 1/10 +1/15 = 1/6
           v = 6 cm          m = -6/-15 = +0.4