Question

if a concave mirror has focal length 10 cm find thw two position where the object can be placed to give in each case an image twice the size of object​

Answer 1

Given :-

▪ A concave mirror of focal length, f = - 10 cm.

To Find :-

▪ The two positions at which the object should be placed to obtain an image twice the size of the object.

Solution :-

Given that the image is twice the size of the object, we know

⇒ Magnification, m = - v/u = h₀ / h

Where,

• v = image distance
• u = object distance
• h₀ = image height
• h = object height

In case first, let's suppose the image we get is real, which means the distance will be negative.

For REAL image, magnification = negative

⇒ -(v) / u = -2

[ Since, Image is twice the size of the object ]

⇒ -v = -2u

⇒ v = 2u

⇒ 1/v = 1/2u ...(1)

For VIRTUAL image, magnification = positive

⇒ -(v) / u = 2

[ Since, The image is twice the size of the Object ]

⇒ -v = 2u

⇒ v = - 2u

⇒ 1/v = -1/2u ...(2)

CASE 1 (REAL IMAGE)

Using the mirror formula, we have

⇒ 1/f = 1/v + 1/u

⇒ -1/10 = 1/2u + 1/u [ from (1) ]

⇒ -1/10 = (1 + 2)/2u

⇒ -1/10 = 3/2u

⇒ -1/5 = 3/u

⇒ u = -15 cm

Case 2 (VIRTUAL IMAGE)

Similarly, using the mirror formula, we have

⇒ 1/f = 1/u + 1/v

⇒ -1/10 = 1/u - 1/2u [ from (2) ]

⇒ -1/10 = (2 - 1)/2u

⇒ -1/10 = 1 / 2u

⇒ 2u = -10

⇒ u = -5 cm

Hence, The two possible positions at which the object can be placed to obtain image twice the size of the object are -15 cm and -5 cm. Here, The negative sign indicates that the object must be placed infront of the mirror.