Question

a concave mirror has focal length 40cm. object distance is 20 cm object height is 5 cm. h' =? m=? v=?​

Answer 1

Answer:

h'=10cm ; m= 2 times ; v = 40

Explanation:

By Mirror Formula

1/f = 1/v + 1/u

By sign cartesian

f= -40cm

u= -20cm

h= 5cm

1/-40 = 1/v + 1/-20

1/-40 = 1/v -1/20

1/-40+1/20 = 1/v

or,

1/20-1/40 = 1/v

1/40 = 1/v

v = 40 cm

Now,

Magnification

-v/u

-40/-20

= 2 times

So,

h'= h × m

h' = 5×2

h' = 10cm. Answer.

Answer 2

Given :

In concave mirror,

Focal length = - 40 cm

Object distance = - 20 cm

Object height = 5 cm

To find :

The image distance, magnification and image height

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,

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

$\dashrightarrow\sf \dfrac{1}{v} + \dfrac{1}{- 20} = \dfrac{1}{ - 40}$

$\dashrightarrow\sf \dfrac{1}{v} - \dfrac{1}{20} = \dfrac{1}{ - 40}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{ - 40} + \dfrac{1}{20}$

$\dashrightarrow\sf \dfrac{1}{v} = - \dfrac{1}{40} + \dfrac{1}{20}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{ - 1 + 2}{40}$

$\dashrightarrow\sf \dfrac{1}{v} = \dfrac{1}{40}$

$\dashrightarrow\sf v = 40 \: cm$

thus, the image distance is 40 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 that is,

$\dashrightarrow\bf m = - \dfrac{v}{u}$

$\dashrightarrow\sf m = - \dfrac{40}{ - 20}$

$\dashrightarrow\sf m = 2$

Thus, the magnification is 2 times.

» The Magnification produced by a mirror is equal to the ratio of the height of the image to the height of the object .i.e.,

$\boxed{ \bf m = \dfrac{h'}{h} }$

where,

• h' denotes height of the image
• h denotes height of the object

by, substituting all the given values in the formula,

$\dashrightarrow \sf m = \dfrac{h'}{h}$

$\dashrightarrow \sf 2 = \dfrac{h'}{5}$

$\dashrightarrow \sf h' = 10 \: cm$

Thus, the image height is 10 cm