Question

a man holds the earth is spherical shaving mirror of radius of curvature 60cm at a distance of 15 cm from his face find the position and nature of image also calculate magnification show ray diagram​

Answer 1

Given :

• Radius of Curvature (R) = 60 cm
• Object Distance (u) = - 15 cm

To Find :

• Nature, Position, size of Image

Solution :

As we know that the mirror used in shaving is Concave Mirror. And we know that focal length of concave mirror is negative, so Radius of Curvature will also be negative,

⇒R = 2f

⇒f = R/2

⇒f = -60/2

⇒f = -30

$\therefore$ Focal length of Concave mirror is -30 cm

_______________________________

Use mirror formula :

⇒1/f = 1/v + 1/u

⇒1/v = 1/f - 1/u

⇒1/v = -1/30 - (-1/15)

⇒1/v = -1/30 + 1/15

⇒1/v = (-1 + 2)/30

⇒1/v = 1/30

⇒v = 30

$\therefore$ Image is produced 30 cm away from mirror .

______________________________

We will use formula for Magnification :

⇒m = -v/u

⇒m = -30/(-15)

⇒m = 30/15

⇒m = 2

• Image is Virtual and Erect
• Size of Image is enlarged.

Answer 2

Answer:

Given :

• Shaving mirror [Concave Mirror]
• Radius of curvature = 60 cm
• Object Distance = 15 cm.

To Find :

• Image Distance.
• Nature of Image.
• Position of Image.
• Size of Image.
• Magnification.

Solution :

If the radius of curvature given is 60 cm, the focal length will be half of it that is 30 cm.

Hence, f = 30 cm.

A concave mirror always have negative focal length and negative object distance.

Hence, f = -30 cm and u = -15 cm.

Mirror Formula : 1/v + 1/u = 1/f.

So, 1/v + (-1/15) = -1/30

➸ 1/v = -1/30 + 1/15

➸ 1/v = (-15 + 30)/450

➸ 1/v = 15/450

➸ 1/v = 1/30

➸ v = 30 cm

The image formed will be behind the mirror at the distance of 30 cm. [Position of the Image]

The image formed will be virtual and erect. [Nature of the image]

The size of the image will be enlarged. [Size of the image]

Now, Finding the magnification of the Image formed :

Formula : m = -v/u.

➸ m = -(30/-15)

➸ m = -(-2/1)

➸ m = 2/1

➸ Magnification = 2.