Question

Where should the object of 4cm
height placed in front of concave mirror
of focal length 12cm whose image
should be 1cm in height.​

Answer 1

Answer: 9 cm infront of the mirror.

The following statements and values are given in the question :-

• Height of object, h = +4 cm (It is always placed on the left side, and above the principal axis and hence always positive. )
• Given kind of mirror is a concave mirror, And we know Focal length of a concave mirror is always negative.
• Focal length, f = - 12 cm

We have to find the distance of the object it should be placed at so to get the image of height, h' = -1 cm. (Concave mirror forms inverted images, unless the object is placed b/w the focus and the pole. )

Now, We don't know u here, But We know, u, v and magnification, m is related by the formula:

⇒ m = v / u

After finding any of the distances, we can find v in terms of u and then substitute it in the mirror formula which is given by :-

• 1/u + 1/v = 1/f

But first, Let's find v in terms of u,

⇒ m = h / h' and m = v / u

So,

⇒ h / h' = v / u

⇒ 4 / -1 = v / u

⇒ 4u = -v

⇒ v = -4u

Substituting the value of v in mirror formula, we get:

⇒ 1/u + (1/-4u) = 1/(-12)

⇒ 1/u - 1/4u = -1/12

⇒ (4 - 1)/4u = -1/12

⇒ 3 × 12 = -1 × 4u

⇒ 36 = -4u

⇒ u = -9 cm

Hence, The object should be placed at the distance of 9 cm infront of the mirror.

Answer 2

Height оf оbjeсt = 4cm

• Fосаl length of concave mirror = -12cm
• Fосаl length of concave mirror = -12cmHeight = 1cm

Formula used :-

m = v/u

Solve :-

1 / u + 1 / v = 1 / f

FIND v IN TERM OF u

m = h /h' аnd m = v/ u

‏‏‎ ‎ h/ h' = v / u

‏‏‎ ‎4 / -1 = v / u

‏‏‎ ‎ 4u = -v

‏‏‎ ‎ v = -4u

V = - 4 u

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Now, substitute it

‏‏‎ ‎1/u + (1 / -4u) = 1/ -12

‏‏‎ ‎1/u - 1/4u = -1/12

‏‏‎ ‎4 - 1/4u = -1/12

‏‏‎ ‎3 X 12 = -1 X 4u

‏‏‎ ‎36 = -4 u

‏‏‎ ‎ = -9 сm

U = - 9 cm

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hope it helps