Question

A diverging lens of focal length 20 cm and a converging lens of focal length 30 cm are placed 15 cm apart with their principal axes coinciding. Where should an object be placed on the principal axis so that its image is formed at infinity?

Answer 1

Given :

Diverging lens focal length=f1=20cm

Converging lens focal length=f2=30cm

Distance between lens =d= 15cm

1/f=1/f1+/f2- d/f1f2

=1/30-1/20 -15/(30)x-20

=1/120

f=120cm

as f is positive it is convex lens

let d1 be the distance from concave lens .

so that emergent beam is parallel to principal axis

and image is formed at infinity

d1= df/fc=15x120/30=60cm

the object should be placed 120-60-60cm from diverging lens

d2=df/fd=15x120/20

d2=90cm

Thus it should be 120+90=210cm right to converging lens

Answer 2

ᴅɪᴠᴇʀɢɪɴɢ ʟᴇɴs ғᴏᴄᴀʟ ʟᴇɴɢᴛʜ=ғ1=20ᴄᴍ

ᴄᴏɴᴠᴇʀɢɪɴɢ ʟᴇɴs ғᴏᴄᴀʟ ʟᴇɴɢᴛʜ=ғ2=30ᴄᴍ

ᴅɪsᴛᴀɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ʟᴇɴs =ᴅ= 15ᴄᴍ

1/ғ=1/ғ1+/ғ2- ᴅ/ғ1ғ2


=1/30-1/20 -15/(30)x-20

=1/120

ғ=120ᴄᴍ

ᴀs ғ ɪs ᴘᴏsɪᴛɪᴠᴇ ɪᴛ ɪs ᴄᴏɴᴠᴇx ʟᴇɴs

ʟᴇᴛ ᴅ1 ʙᴇ ᴛʜᴇ ᴅɪsᴛᴀɴᴄᴇ ғʀᴏᴍ ᴄᴏɴᴄᴀᴠᴇ ʟᴇɴs .


sᴏ ᴛʜᴀᴛ ᴇᴍᴇʀɢᴇɴᴛ ʙᴇᴀᴍ ɪs ᴘᴀʀᴀʟʟᴇʟ ᴛᴏ ᴘʀɪɴᴄɪᴘᴀʟ ᴀxɪs


ᴀɴᴅ ɪᴍᴀɢᴇ ɪs ғᴏʀᴍᴇᴅ ᴀᴛ ɪɴғɪɴɪᴛʏ


ᴅ1= ᴅғ/ғᴄ=15x120/30=60ᴄᴍ


ᴛʜᴇ ᴏʙᴊᴇᴄᴛ sʜᴏᴜʟᴅ ʙᴇ ᴘʟᴀᴄᴇᴅ 120-60-60ᴄᴍ ғʀᴏᴍ ᴅɪᴠᴇʀɢɪɴɢ ʟᴇɴs


ᴅ2=ᴅғ/ғᴅ=15x120/20


ᴅ2=90ᴄᴍ


ᴛʜᴜs ɪᴛ sʜᴏᴜʟᴅ ʙᴇ 120+90=210ᴄᴍ ʀɪɢʜᴛ ᴛᴏ ᴄᴏɴᴠᴇʀɢɪɴɢ ʟᴇɴs