Question

A telescope made of mirrors is used to observe the moon. It forms the inverted image of the moon at 3.5 km from the eye piece. Find the diameter of the image of the moon. Given the diameter of the moon is 1700 km and the distance of the moon from the earth is 350,000 km.​

Answer 1

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

✒ ᴀɴsᴡᴇʀ:-

⛄ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴍᴏᴏɴ's ɪᴍᴀɢᴇ = 17 ᴍ.

✒ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

⛄ ɢɪᴠᴇɴ:-

★ ʜ = ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴍᴏᴏɴ = 1700 ᴋᴍ.

★ ᴜ = 350,00 ᴋᴍ ᴅɪsᴛᴀɴᴄᴇ ᴏғ ᴍᴏᴏɴ ғʀᴏᴍ ᴛʜᴇ ᴇᴀʀᴛʜ

(ᴏʙᴊᴇᴄᴛ ᴅɪsᴛᴀɴᴄᴇ)

★ ᴠ = 3.5 ᴋᴍ ᴅɪsᴛᴀɴᴄᴇ ᴏғ ɪᴍᴀɢᴇ ᴏғ ᴍᴏᴏɴ ғʀᴏᴍ ᴛʜᴇ ᴇᴀʀᴛʜ. (ɪᴍᴀɢᴇ ᴅɪsᴛᴀɴᴄᴇ)

ʟᴇᴛ ʜ' ʙᴇ ᴛʜᴇ ɪᴍᴀɢᴇ ᴅɪsᴛᴀɴᴄᴇ ɪ.ᴇ., ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴍᴏᴏɴ's ɪᴍᴀɢᴇ ᴀɴᴅ ᴍ ʙᴇ ᴛʜᴇ ᴍᴀɢɴɪғɪᴄᴀᴛɪᴏɴ.

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

ᴍ = ʜ'/ʜ = - ᴠ/ᴜ

ᴏɴ sᴜʙsᴛɪᴛᴜᴛɪɴɢ ᴛʜᴇ ɢɪᴠᴇɴ ᴠᴀʟᴜᴇs ᴡᴇ ɢᴇᴛ,

ʜ'/1700 = -3.5/350000

ʜ' = -17 × 10^-3 ᴋᴍ = -17 ᴍ.

ᴛʜᴇ ɴᴇɢᴀᴠɪᴛɪᴠᴇ sɪɢɴ sʜᴏᴡs ᴛʜᴀᴛ ᴛʜᴇ ɪᴍᴀɢᴇ ᴏғ ᴛʜᴇ ᴍᴏᴏɴ ɪs ɪɴᴠᴇʀᴛᴇᴅ.

ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴍᴏᴏɴ's ɪᴍᴀɢᴇ = 17 ᴍ.

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Answer 2

Answer:

✒ ᴀɴsᴡᴇʀ:-

⛄ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴍᴏᴏɴ's ɪᴍᴀɢᴇ = 17 ᴍ.

✒ ᴇxᴘʟᴀɴᴀᴛɪᴏɴ:-

⛄ ɢɪᴠᴇɴ:-

★ ʜ = ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴍᴏᴏɴ = 1700 ᴋᴍ.

★ ᴜ = 350,00 ᴋᴍ ᴅɪsᴛᴀɴᴄᴇ ᴏғ ᴍᴏᴏɴ ғʀᴏᴍ ᴛʜᴇ ᴇᴀʀᴛʜ

(ᴏʙᴊᴇᴄᴛ ᴅɪsᴛᴀɴᴄᴇ)

★ ᴠ = 3.5 ᴋᴍ ᴅɪsᴛᴀɴᴄᴇ ᴏғ ɪᴍᴀɢᴇ ᴏғ ᴍᴏᴏɴ ғʀᴏᴍ ᴛʜᴇ ᴇᴀʀᴛʜ. (ɪᴍᴀɢᴇ ᴅɪsᴛᴀɴᴄᴇ)

ʟᴇᴛ ʜ' ʙᴇ ᴛʜᴇ ɪᴍᴀɢᴇ ᴅɪsᴛᴀɴᴄᴇ ɪ.ᴇ., ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴍᴏᴏɴ's ɪᴍᴀɢᴇ ᴀɴᴅ ᴍ ʙᴇ ᴛʜᴇ ᴍᴀɢɴɪғɪᴄᴀᴛɪᴏɴ.

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

ᴍ = ʜ'/ʜ = - ᴠ/ᴜ

ᴏɴ sᴜʙsᴛɪᴛᴜᴛɪɴɢ ᴛʜᴇ ɢɪᴠᴇɴ ᴠᴀʟᴜᴇs ᴡᴇ ɢᴇᴛ,

ʜ'/1700 = -3.5/350000

ʜ' = -17 × 10^-3 ᴋᴍ = -17 ᴍ.

ᴛʜᴇ ɴᴇɢᴀᴠɪᴛɪᴠᴇ sɪɢɴ sʜᴏᴡs ᴛʜᴀᴛ ᴛʜᴇ ɪᴍᴀɢᴇ ᴏғ ᴛʜᴇ ᴍᴏᴏɴ ɪs ɪɴᴠᴇʀᴛᴇᴅ.

ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴍᴏᴏɴ's ɪᴍᴀɢᴇ = 17 ᴍ.