Question

An object is placed at a distance of 16cm in front of a concave
mirror. It forms a real image four times larger than the object.
Calculate the distance of the image from the mirror.

Answer 1

Given:-

• Object Distance (u) = 16 cm
• Size of image is four times the size of the object.
• Mirror used = Concave Mirror.

To Find:-

• Image distance from the mirror.

Solution:-

According to sign convention:-

• Object distance is always negative.

Hence,

• Object distance (u) = -16

Now,

According to the magnification of a concave mirror,

• If the image formed is real then the magnification will be negative.

As stated in the question,

• Image formed is real and is four times the size of the object.

Hence,

• Magnification = -4

Now,

We know,

m = $\sf{-\dfrac{v}{u}}$

Where,

• v = image distance
• u = object distance
• m = magnification

Now,

Putting all the values in the formula of magnification:-

= -4 = $\sf{\dfrac{-v}{-16}}$

= -4 = $\sf{ \dfrac{\not{-v}}{\not{-16}}}$

= -4 × 16 = v

=> v = -64 cm

∴ The distance of the image from the mirror is 64 cm.

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Explore More!!!!

Let us know more about magnification of concave mirror.

Formula for finding magnification when the height of image and height of object is given is:-

• m = $\sf{\dfrac{h'}{h}}$

Where:-

• h' = height of image
• h = height of object

Some other points:-

• If the magnification of the mirror come negative then the image of the object formed is always real and inverted.

• If the magnification of the mirror comes positive then the image of the object formed is always virtual and erect.

Note:- This is applicable for both Concave and Convex mirror.

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Answer 2

Answer:

Given:-

Object Distance (u) = 16 cm

Size of image is four times the size of the object.

Mirror used = Concave Mirror.

To Find:-

Image distance from the mirror.

Solution:-

According to sign convention:-

Object distance is always negative.

Hence,

Object distance (u) = -16

Now,

According to the magnification of a concave mirror,

If the image formed is real then the magnification will be negative.

As stated in the question,

Image formed is real and is four times the size of the object.

Hence,

Magnification = -4

Now,

We know,

$m = \sf{-\dfrac{v}{u}}− </p><p>u</p><p>v$

Where,

v = image distance

u = object distance

m = magnification

Now,

Putting all the values in the formula of magnification:-

= -4 × 16 = v

=> v = -64 cm

∴ The distance of the image from the mirror is 64 cm.

________________________________

Explore More!!!!

Let us know more about magnification of concave mirror.

Formula for finding magnification when the height of image and height of object is given is:-

$m = \sf{\dfrac{h'}{h}} </p><p>h</p><p>h </p><p>′$

Where:-

h' = height of image

h = height of object

Some other points:-

If the magnification of the mirror come negative then the image of the object formed is always real and inverted.

If the magnification of the mirror comes positive then the image of the object formed is always virtual and erect.

Note:- This is applicable for both Concave and Convex mirror.

________________________________