Question

If a concave mirror has a focal length of 10cm find the position where an object can be placed to give in each case an image twice the height of the object

Answer 1

The  image twice the height of the object can
1) Virtual,erect and enlarged      or   2) Real,inverted and enlarged
1) Virtual,erect and enlarge  , in this we will take m = 2
now , m = - v / u 
             2 = - v / u 
           2u = -v                            therefore , v = -2u
1 / f                = (1 / v) + (1 / u )
1 / (-10)      = 1 / (-2u) + 1 / u 
1 / - 10         = - 1 + 2 / 2u
1 / - 10        =  1 / 2u 
- 10              =  2u                  therefore , u  = - 5 cm 
2)  2) Real,inverted and enlarge , 
in this we will take,  m = -2
now , m = - v / u 
             -2 = - v / u 
           - 2u = -v                            therefore , v = 2u 
1 / f                = (1 / v )+ (1 / u) 
1 / (-10)      = 1 / (2u) + 1 / u 
1 / - 10         = (1 + 2) / 2u
1 / - 10        =  3 / 2u 
- 30              =  2u                  therefore , u  = - 15 cm 
Therefore, an image twice the height of the object can be obtained when the object is placed at
 1. 5cm from the concave mirror
2.15cm from the concave mirror

Answer 2

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