Question

 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.

Answer 1

 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