Question

A 9 cm tall object was placed 27 cm in front of a concave mirror of focal length 18 cm. The image distance and the size of the image respectively (with correct sign convention) will be:​

Answer 1

Given :

In concave mirror,

Height of object : 9 cm.

Object distance : 27 cm.

Focal length : 18 cm.

To find :

The image distance and the size of the image.

Solution :

Using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

$\boxed{\bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}}$

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

By substituting all the given values in the formula,

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{ - 27} = \dfrac{1}{ - 18}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{27} = \dfrac{1}{ - 18}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{ - 18} + \dfrac{1}{27}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 3 + 2}{54}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 1}{54}$

$\dashrightarrow\sf v = - 54 \: cm$

Thus, the position of the image is -54 cm.

We know that,

» The linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign and it is equal to the ratio of image height and object height. that is,

$\boxed{\bf m = \dfrac{h'}{h} = - \dfrac{v}{u}}$

where,

• h' denotes height of image
• h denotes object height
• v denotes image distance
• u denotes object distance

By substituting all the given values in the formula,

$\dashrightarrow\sf \dfrac{h'}{h} = - \dfrac{v}{u}$

$\dashrightarrow\sf \dfrac{h'}{9} = - \dfrac{ - 54}{ - 27}$

$\dashrightarrow\sf \dfrac{h'}{9} = - 2$

$\dashrightarrow\sf h'= - 2 \times 9$

$\dashrightarrow\sf h'= - 18 \: cm$

Thus, the height of the image is -18 cm.

Answer 2

Answer:

The correct answer is -18

Explanation:

Given :

In concave mirror,

Height of object : 9 cm.

Object distance : 27 cm.

Focal length : 18 cm.

To find :

The image distance and the size of the image.

Solution :

Using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

where,

v denotes Image distance

u denotes object distance

f denotes focal length

By substituting all the given values in the formula,

Thus, the position of the image is -54 cm.

We know that,

» The linear magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign and it is equal to the ratio of image height and object height. that is,

where,

h' denotes height of image

h denotes object height

v denotes image distance

u denotes object distance

By substituting all the given values in the formula,

Thus, the height of the image is -18 cm.

If the image and object are on the same side of the lens, the image distance is negative and the image is virtual. For converging mirrors, the focal length is positive. Similarly, a converging lens always has a positive f, and a diverging lens has a negative f.

The focal length of a concave mirror is negative because the focus of a concave mirror is in front of the mirror, on the left side. Whereas, The focal length of a convex mirror is positive because the focus of a convex mirror is behind the mirror, on the right side.

What is focal length of concave mirror? ​

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A 9 cm tall object was placed 27 cm in front of a concave mirror of focal length 18 cm

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