Question

a diverging mirror of radius of curvature 40cm forms an image which is half the height of the object. find the object and image position.

Answer 1

Data:
Radius of curvature = R = 40 cm
We have to find the position of object and image.
Let U be the position of an object and V be the position of an image.
Then,
U = ?
V = ?
Also suppose that, h₁ and h₂ be the height of object and height of image respectively.
Then, according to the given condition, the height of image is half of the height of object.
Therefore, h₂ = h₁ / 2
Also, we know that, 
- V / U = h₂ / h₁
- V / U = (h₁ / 2) / h₁
- V / U = 1 / 2
2 V = - U  
V = - U / 2   ......... (1)
Now we use the mirror formula,
1 / V + 1 / U = 1 / f
1 / V + 1 / U = 2 / R
1 / (-U/2) + 1 / U = 2 / R  ,   Using equation (1)
- 2 / U + 1 / U = 2 / 40
- 1 / U = 1 / 20
U = - 20 cm
Now,
V = - U / 2 = - (-20) / 2
V = 10 cm
which is the required answer.
Hope it helps. Thanks.

Answer 2

Hey mate here is ur answer.....

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HOPE IT HELPS YOU.....