Answer 1

Here, filament of the lamp acts as an object.

v = Image distance

and u = Object distance

According to the question:

v + u = 80 (taking magnitude only)        ...(i)

and magnification m = `"v"/"u"` = 3

or, v = 3 u

or, v - 3u  = 0          ...(ii)

Solving (i) and (ii), we get:

u = 20 cm

For the focal length of the lens, we have:

Distance of lens from the filament, u = -20 cm

`"v"=3 xx "u"=3 xx 20 = 60`cm

Applying lens formula, we get:

`1/"v" -1/"u" = 1/"f"`

`1/60 + 1/20 = 1/"f"`

`(1+3)/60= 1/"f"`

`1/"f"=4/60`

f=15 cm

So, focal length f = 15 cm