Question

Use the mirror equation to show a convex mirror always produces a virtual image independent of the location of the object ?

Answer 1

A convex mirror

f > 0; u < 0 (always)

Case I |u| > |f|

We know,

`v =(fu)/(u-f)`

`fu <0 and f-u<0`

`=> v>0 `  virtual image

Case `2|u|<|f|`

`v=(fu)/(u-f)     fu<0`

`=> u> 0           u-f<0`

Hence, at all the positions convex mirror will form a virtual image.