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If a concave mirror has a …

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

  • 2 answers

Naveen Sharma 7 years, 2 months ago

Given f = -10 cm

magnification is twice so taking

m = +2 and -2m = -v/u

2 = -v/u

v = -2u

1/f = 1/v + 1/u

-1/10 = -1+2/2u

u = -5

Now taking magnification as -2

m = -v/u

-2 = -v/u

v = 2u

1/f = 1/v + 1/u

-1/10 = (1+2)/2u

-2u = 30 or

u = -15

Payal Singh 7 years, 2 months ago

Ans.

The image twice the height of the object can

A) Virtual,erect and enlarged

Or

B) 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, u=-5 cm 

 B) 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

 A) 5cm from the concave mirror

B) 15cm from the concave mirror

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