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?
Answers
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.