Question

An object of 5 centimetre is placed in front of mirror of focal length 30 cm if the elected image formed at a distance of 10 cm behind the mirror find the object distance and size of the image.​

Answer 1

Answer :

• Object distance is -7.5 cm
• Height of the image is - 1.25 cm

Explanation :

Given :

• Height of the object, hᵢ = 5 cm
• Focal length of the mirror, f = 30 cm
• Image distance, v = 10 cm

To find :

• Object distance, u = ?
• Height of the image, hₒ = ?

Knowledge required :

• Mirror formula :

⠀⠀⠀⠀⠀⠀⠀⠀⠀1/f = 1/v + 1/u⠀

[Where : f = Focal length of the mirror, v = Image distance, u = Object Distance]

• Magnification :

⠀⠀⠀⠀⠀⠀⠀⠀⠀m = - v/u = hᵢ/hₒ⠀

[Where: m = Magnification, v = Image distance, u = Object Distance, hᵢ = Height of the image, hₒ = Height of the object]

Solution :

To find the object distance of the mirror :

⠀⠀By using the mirror formula and substituting the values in it, we get :

⠀⠀=> 1/f = 1/v + 1/u

⠀⠀=> 1/(-30) = 1/10 + 1/u ⠀⠀⠀⠀[∴ By sign convention, f = (-30) cm]

⠀⠀=> 1/(-30) - 1/10 = 1/u

⠀⠀=> 1/(-30) - 1/10 = 1/u

⠀⠀=> (-1 - 3)/30 = 1/u

⠀⠀=> (-4)/30 = 1/u

⠀⠀=> u = 30/(-4)

⠀⠀=> u = (-7.5)

⠀⠀⠀⠀⠀⠀∴ u = (-7.5) cm

Therefore,

• Object distance, u = (-7.5) cm

To find the image height :

By using the formula for magnification and substituting the values in it, we get :

⠀⠀=> m = - v/u = hᵢ/hₒ

⠀⠀=> - (-7.5)/(-30) = hᵢ/5

⠀⠀=> - 75/300 = hᵢ/5

⠀⠀=> - 75 × 5 = hᵢ × 300

⠀⠀=> - 375 = hᵢ × 300

⠀⠀=> - 375/300 = hᵢ

⠀⠀=> - 1.25 = hᵢ

⠀⠀⠀⠀⠀⠀∴ u = (-1.25) cm

Therefore,

• Height of the image, hₒ = - 1.25 cm

Answer 2

$\huge{\boxed{\bold{Question}}}$

An object of 5 centimetre is placed in front of

mirror of focal length 30 cm if the elected image

formed at a distance of 10 cm behind the mirror

find the object distance and size of the image.

$\huge{\boxed{\bold{Answer}}}$

Given,

•height of the object h¡=5cm

•focal length of the mirror, F=30cm

•image distance v=10cm

To find

•object distance=?

•height of the image h_o=?

Solution

(1)

1/f=1/v+1/v

1/(-30)=1/10+1/v

1/(-30)-1/10=1/v

1/(-30)-1/10=1/v

(-1-3)/30=1/v

(-4)/30=1/v

v=30/(-4)

v=(-7.5)

v=(-7.5)cm

(2)

m=-v/u=h¡/h_o

(1(-7.5)/(30)=h¡/5

-75/300=h¡/5

-75×5=h¡×300

-375=h¡×300

-375/300=h¡

-1.25=h¡

u=(-1.25)cm