Question

an object 4.0 cm in size is placed at 25.0cm of concave mirror of focal length 15.0 cm .at what distance from the mirror should a screen be placed in order to obtain a sharp image ? find the nature and size of image.

Answer 1

Refer the picture.

Hope it helps.

Answer 2

ʜᴇʏᴀ ᴍᴀᴛᴇ!!

ʜᴇʀᴇ ɪs ᴜʀ ᴀɴsᴡᴇʀ ⏬⏬

ɢɪᴠᴇɴ,

sɪᴢᴇ ᴏғ ᴏʙᴊᴇᴄᴛ , ʜ₀ = 4ᴄᴍ

ᴏʙᴊᴇᴄᴛ ᴅɪsᴛᴀɴᴄᴇ , ᴜ = -25ᴄᴍ

ғᴏᴄᴀʟ ʟᴇɴɢᴛʜ ᴏғ ᴄᴏɴᴄᴀᴠᴇ ᴍɪʀʀᴏʀ , ғ = -15ᴄᴍ

ᴜsᴇ ғᴏʀᴍᴜʟᴀ ,

1/ᴠ + 1/ᴜ = 1/ғ

⇒1/ᴠ + 1/-25 = 1/-15

⇒1/ᴠ = 1/-15 + 1/25 = (-25 + 15)/375 = 1/-37.5 ᴄᴍ

⇒ ᴠ = - 37.5 ᴄᴍ ,

∴ ɪᴍᴀɢᴇ ɪs ғᴏʀᴍᴇᴅ ᴏʙᴊᴇᴄᴛ sɪᴅᴇ , 37.5ᴄᴍ ғʀᴏᴍ ᴘᴏʟᴇ ᴏғ ᴄᴏɴᴄᴀᴠᴇ ᴍɪʀʀᴏʀ.

ɴᴏᴡ, ᴜsᴇ ғᴏʀᴍᴜʟᴀ,

ʜɪ/ʜ₀ = -ᴜ/ᴠ

ᴡʜᴇʀᴇ ʜɪ ɪs ᴛʜᴇ sɪᴢᴇ ᴏғ ɪᴍᴀɢᴇ .

ɴᴏᴡ, ʜɪ/4ᴄᴍ = -(-37.5ᴄᴍ)/(-25ᴄᴍ)

ʜɪ = -4 × 37.5/25 ᴄᴍ = -6ᴄᴍ

∴ sɪᴢᴇ ᴏғ ɪᴍᴀɢᴇ = 6ᴄᴍ

ʜᴇɴᴄᴇ,sʀᴇᴇɴ sʜᴏᴜʟᴅ ᴘʟᴀᴄᴇ 37.5 ᴄᴍ ʟᴇғᴛ sɪᴅᴇ ᴏғ ᴍɪʀʀᴏʀ ᴀɴᴅ sɪᴢᴇ ᴏғ ɪᴍᴀɢᴇ ɪs 6ᴄᴍ .ɪᴛ ɪs ɪɴᴠᴇʀᴛᴇᴅ ᴀɴᴅ ʟᴀʀɢᴇʀ ᴛʜᴀɴ ᴏʙᴊᴇᴄᴛ's sɪᴢᴇ.