Question

How far should an object be placed from a convex lens of focal length 20 cm to obtain its image at a distance of 30 cm from the lens?

What will be the height of the image if the object is 6 cm tall?​

Answer 1

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$\huge\fcolorbox{black}{aqua}{Solution:-}$

✒ ᴀɴsᴡᴇʀ:-

⛄ ★ object distance, u = -60 cm.

★ height of the image, h= -3 cm.

✒ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

⛄ ɢɪᴠᴇɴ:-

★ ғᴏᴄᴀʟ ʟᴇɴɢᴛʜ, ғ = + 20 ᴄᴍ.

★ ɪᴍᴀɢᴇ ᴅɪsᴛᴀɴᴄᴇ, ᴠ = +30 ᴄᴍ.

★ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ᴏʙᴊᴇᴄᴛ, ʜ= +6 ᴄᴍ.

★ ᴏʙᴊᴇᴄᴛ ᴅɪsᴛᴀɴᴄᴇ, ᴜ = ?

★ ʜᴇɪɢʜᴛ ᴏғ ᴛʜᴇ ɪᴍᴀɢᴇ, ʜ' = ?

ᴜsɪɴɢ ʟᴇɴs ғᴏʀᴍᴜʟᴀ, 1/ғ = 1/ᴠ - 1/ᴜ

=) 1/ᴜ = 1/ᴠ - 1/ғ

= 1/+30 - 1/+20 = 1/30 - 1/20

= 2 - 3/60

= -1/60

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴜ= - 60 ᴄᴍ.

ɴᴏᴡ, ᴍ = ʜ'/ʜ = ᴠ/ᴜ

ᴛʜᴇʀᴇғᴏʀᴇ,

ʜ' = ᴠ/ᴜ × ʜ = +30/-60 × (+6)

ʜ' = -3 ᴄᴍ.

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