Question

The object 2.5cm heigh is placed at a distance of 10cm from a concave mirror of radius of curvature 30cm the size of the object is​

Answer 1

Answer :

Height of object = 2.5cm

Distance of object = 10cm

Radius of curvature = 30cm

Type of mirror : concave

$\star$ First we need to find focal length of mirror.

We know that, R = 2f

⭆ f = R/2

⭆ f = 30/2

⭆ f = 15 cm

Focal length of concave mirror is taken negative.

★ Position of image :

➝ 1/u + 1/v = 1/f

➝ 1/(-10) + 1/v = 1/(-15)

➝ 1/v = -1/15 + 1/10

➝ 1/v = (-2 + 3)/30

➝ v = 30 cm

★ Size of image :

➝ m = -v/u = h'/h

• h' denotes height of images
• h denotes height of object

➝ -30/-10 = h'/2.5

➝ h' = 3 × 2.5

➝ h' = 7.5 cm

★ Nature of image :

• Virtual
• Erect
• Enlarged

Answer 2

Given :-

• Height of the object (ho)= 2.5 cm

• Object distance(u) = - 10 cm

( Distances are measured from the pole of the mirror )

• Radius of curvature(R) = - 30 cm (concave mirror )

To find :-

• Size of image (hi)

Solution :-

Step I:- focal length of the mirror

we know that ,

⟹ f = R / 2

⟹ f = - 30 /2

⟹ f = - 15 cm

( focal length of a concave mirror is always negative )

Step II :- Image distance

By using the  mirror formula ,

⟹  1 / f = 1 / u + 1 / v

On rearranging ,

⟹ 1 / v = 1 / f - 1 / u

⟹ 1 / v = 1 / -15 - 1 / (-10)

⟹ 1 / v = - 1 / 15 + 1 /10

⟹ 1 /v = -2 + 3 / 30

⟹ 1 / v = 1 / 30

⟹ v =30 cm

Step III :- Size of object

A per the formula ,

⟹ m = - v / u = hi / ho

⟹ - v /u = hi / ho

⟹ hi = -v /u x ho

⟹ hi = - 30 / - 10 x 2.5

⟹ hi = 3 x 2.5

⟹ hi = 7.5 cm

The size of the image is 7.5 cm