Question

The image formed by a spherical mirror is real, inverted and is of magnification −2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.

Answer 1

Given: 

• Nature: Spherical mirror (concave)
• Image is real and inverted
• Magnification (m) = -2
• Image distance (v) = -30 cm

Step 1: Find the object distance (u)

Using the magnification formula: 

`m = -v/u`

`=> -2 = -(-30)/u`

`=> 2 = 30/u`u = 15 cm

So, the object distance = −15 cm
(Negative sign shows it is in front of the mirror)

Step 2: Use mirror formula to find focal length (f)

Mirror formula: 

`1/f = 1/v + 1/u`

`1/f = 1/(-30) + 1/(-15)`

`(-1)/30 + (-2)/30`

`(-3)/30 => f = -10` cm

So, the focal length = −10 cm (Concave mirror)

Step 3: Move the object 10 cm closer to the mirror

New object distance:

u' = −15 + 10 = −5 cm

Using the mirror formula:

`1/v = 1/f - 1/u`

= `1/(-10) - 1/(-5)`

= `-1/10 + 1/5 = 1/10`

v = 10 cm

So, the image is formed 10 cm behind the mirror (positive v).

Step 4: Find the new magnification 

`m = -v/u = -10/(-5) = 2`

Focal length of the mirror = −10 cm

The image becomes virtual, erect and magnified.