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.

Answers:

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
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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 = vtherefore, 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 cmB) Real,inverted and enlarge ,
in this we will take, m = 2
now,m =  v / u
2 =  v / u
 2u = vtherefore , 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 cmTherefore, 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
Thanks (1)