An object 3 cm high is placed 24 cm away from a convex lens of focal length 8 cm. Find by calculations, the position, height and nature of the image.
Solution
Given:
Object distance (u) =-24
Focal length (f) = +8
Object height (h) = 3 Lens formula is given by:1f=1v-1u⇒18=1v-1-24⇒18=1v+124⇒18-124=1v⇒3-124=1v⇒224=1v ⇒ v=12 cm Image will be form at a distance of 12 cm on the right side of the convex lens.Magnification m=vu ⇒ m=12-24
⇒m=-12So, the image is diminished. Negative value of magnification shows that the image will be real and inverted.">
Lens formula is given by :
`1/f=1/v-1/u`
`1/8=1/v-1/-24`
`1/8=1/v+1/24`
`1/8-1/24=1/v`
`(3-1)/24=1/v`
`2/24=1/v`
`v=12 cm`
Image will be form at a distance of 12 cm on the right side of the convex lens.
Magnification m `v/u`
`m=12/-24`
`m =-1/2`
so, the image is diminished
Negative value of magnification shows that the image will be real and inverted.
`m=h_i/h_o`
`-1/2=h_i/3`
`h_i =-3/2`
`h_i=-1.5` cm
Hight of the image will be 1.5 cm Here, negative sign shows that the image will be in the downard direction
