Question

if an object of 7cm height is placed at a distance of 12 cm form a convex lens of focal length 12cm find the position ,nature and height of the image?

Answer 1

Answer :

• Position of the Image or image distance, v = 0 cm
• Height of the image, hᵢ = 0 cm

Explanation :

Given :

• Height of the object, hₒ = 7 cm
• Object distance, u = 12 cm
• Focal length of the mirror, f = 12 cm

To find :

• Position of the Image or image distance, v = ?
• Nature of the image.
• Height of the image, hᵢ = ?

Knowledge required :

• Lens formula :

⠀⠀⠀⠀⠀⠀⠀⠀⠀1/f = 1/v - 1/u⠀

[Where, f, v and u are the focal length of the mirror, Image distance, Object distance]

• Magnification in a lens '

⠀⠀⠀⠀⠀⠀⠀⠀⠀m = v/u = hᵢ/hₒ⠀

[Where, v, u, hᵢ and h ₒ are the Image distance, Object distance, height of the image and height of the object, respectively]

Solution :

To find the image distance of the mirror :

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

⠀⠀=> 1/f = 1/v - 1/u

⠀⠀=> 1/2 = 1/v - 1/(-12)

⠀⠀=> 1/12 = 1/v + 1/12

⠀⠀=> 1/12 - 1/12 = 1/v

⠀⠀=> 0 = v

⠀⠀⠀⠀∴ v = 0 cm

Hence the image distance of the lens is 0 cm.

Thus the image formed is at infinity.

To find the height of the image :

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

⠀⠀=> v/u = hᵢ/hₒ

⠀⠀=> 0/(-12) = hᵢ/7

⠀⠀=> 0 = hᵢ/7

⠀⠀=> 0 × 7 = hᵢ

⠀⠀=> 0.= hᵢ

⠀⠀⠀⠀∴ hᵢ = 0 cm

Hence the height of the Image is 0 cm.

Nature of the image :

• The image is virtual.
• The image is formed at infinity.