Question

An object of height 7 cm is kept at a distance of 25 cm in front of a concave mirror. The focal length of the mirror is 15 cm. At what distance from the mirror should a screen be kept so as to get a clear image? What will be the size and nature of the image?

Answer 1

Given Data:

• Object height (ho) = 7 cm
• Object distance (u) = −25 cm (since the object is in front of the concave mirror, it is taken as negative)
• Focal length (f) = −15 cm (concave mirror has a negative focal length)

Step 1: Find the Image Distance v

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

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

`1/v = 1/-15 - 1/-25`

`1/v = 1/-15 + 1/25`

`1/v = (-5+3)/75 = (-2)/75`

v = −37.5 cm

Step 2: Find the Size of the Image

Using the magnification formula:

`m = -v/u`

`m = -(-37.5)/-25`

= −1.5

Now, calculating the image height:

h_image​ = m × h_object​

h_image​ = −1.5 × 7

= −10.5 cm

Step 3: Nature of the Image

• Since v is negative, the image is real and inverted.
• Since magnification ∣m∣ = 1.5 is greater than 1, the image is magnified.