Question

ᴀɴ ᴏʙᴊᴇᴄᴛ ᴏꜰ ʜᴇɪɢʜᴛ 4.0 ᴄᴍ ɪꜱ ᴘʟᴀᴄᴇᴅ ᴀᴛ ᴀ ᴅɪꜱᴛᴀɴᴄᴇ ᴏꜰ 30 ᴄᴍ ꜰʀᴏᴍ ᴛʜᴇ ᴏᴘᴛɪᴄᴀʟ ᴄᴇɴᴛʀᴇ 'ᴏ' ᴏꜰ ᴀ ᴄᴏɴᴠᴇx ʟᴇɴꜱ ᴏꜰ ꜰᴏᴄᴀʟ ʟᴇɴɢᴛʜ 20 ᴄᴍ. ᴅʀᴀᴡ ᴀ ʀᴀʏ ᴅɪᴀɢʀᴀᴍ ᴛᴏ ꜰɪɴᴅ ᴛʜᴇ ᴘᴏꜱɪᴛɪᴏɴ ᴀɴᴅ ꜱɪᴢᴇ ᴏꜰ ᴛʜᴇ ɪᴍᴀɢᴇ ꜰᴏʀᴍᴇᴅ. ᴍᴀʀᴋ ᴏᴘᴛɪᴄᴀʟ ᴄᴇɴᴛʀᴇ 'ᴏ' ᴀɴᴅ ᴘʀɪɴᴄɪᴘʟᴇ ꜰᴏᴄᴜꜱ 'ꜰ' ᴏɴ ᴛʜᴇ ᴅɪᴀɢʀᴀᴍ. ᴀʟꜱᴏ ꜰɪɴᴅ ᴛʜᴇ ᴀᴘᴘʀᴏxɪᴍᴀᴛᴇ ʀᴀᴛɪᴏ ᴏꜰ ꜱɪᴢᴇ ᴏꜰ ᴛʜᴇ ɪᴍᴀɢᴇ ᴛᴏ ᴛʜᴇ ꜱɪᴢᴇ ᴏꜰ ᴛʜᴇ ɪᴍᴀɢᴇ.

Answer 1

$\huge\underline{ \mathbb\red{✰A} \green{n} \mathbb\blue{S} \purple{w} \mathbb \orange{E} \pink{r}} \:$

Object distance

$u= −30 cm$

Focal length of convex lens

$f=20 cm$

Height of object

${h}^{o} = 4cm$

Using lens formula :

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$∴   \frac{1}{v} − \frac{1}{ - 30} = \frac{1}{20} </p><p></p><p></p><p>$

$⟹ v=60 cm$

Magnification

$\frac{ {h}^{i} } {ho} = \frac{v}{u} </p><p>$

$⟹  \frac{hi}{4} = \frac{60}{ - 30} </p><p></p><p></p><p> \\ ⟹ hi=−8 cm</p><p></p><p>$

Ratio of size of image to that of object

$\frac{hi}{ho} = \frac{8}{4} = 2$

Hence the answer will be

$2$

Answer 2

Answer:

Object distance

u= −30 cmu=−30cm

Focal length of convex lens

f=20 cmf=20cm

Height of object

{h}^{o} = 4cmh

o

=4cm

Using lens formula :

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

v

⟹ hi=−8 cm