Question

The diameter of the sun is 1.4 × 109 m and its distance from the earth is 1.5 × 1011 m. Find the radius of the image of the sun formed by a lens of focal length 20 cm.

Answer 1

given :

diameter of the sun is 1.4 × 10⁹ m

distance from the earth is=u= - 1.5 × 10¹¹ m

f=20cm

1/f=1/v-1/u

1/v= 1/f+1/u

=1/20 -1/1.5 × 10¹¹

object distance is more compared to focal length. Hence image is formed at Infinity.

=1/20 - 1/1.5 × 10¹¹

on solving we get :

v=1.50 x 10¹¹/7.50x 10⁹

m= v/u=hi/ho

hi= hox v/u

= 1.5 x 10¹¹/7.50 x 10 ⁹ x 1.5 x 10¹¹ ] x 0.7 x 10¹² mm

=0.93 mm

Hence required radius of image of sun is 0.93mm

Answer 2

ᴅɪᴀᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ sᴜɴ ɪs 1.4 × 10⁹ ᴍ

ᴅɪsᴛᴀɴᴄᴇ ғʀᴏᴍ ᴛʜᴇ ᴇᴀʀᴛʜ ɪs=ᴜ= - 1.5 × 10¹¹ ᴍ

ғ=20ᴄᴍ

1/ғ=1/ᴠ-1/ᴜ

1/ᴠ= 1/ғ+1/ᴜ

=1/20 -1/1.5 × 10¹¹

ᴏʙᴊᴇᴄᴛ ᴅɪsᴛᴀɴᴄᴇ ɪs ᴍᴏʀᴇ ᴄᴏᴍᴘᴀʀᴇᴅ ᴛᴏ ғᴏᴄᴀʟ ʟᴇɴɢᴛʜ. ʜᴇɴᴄᴇ ɪᴍᴀɢᴇ ɪs ғᴏʀᴍᴇᴅ ᴀᴛ ɪɴғɪɴɪᴛʏ.

=1/20 - 1/1.5 × 10¹¹

ᴏɴ sᴏʟᴠɪɴɢ ᴡᴇ ɢᴇᴛ :

ᴠ=1.50 x 10¹¹/7.50x 10⁹

ᴍ= ᴠ/ᴜ=ʜɪ/ʜᴏ

ʜɪ= ʜᴏx ᴠ/ᴜ

= 1.5 x 10¹¹/7.50 x 10 ⁹ x 1.5 x 10¹¹ ] x 0.7 x 10¹² ᴍᴍ

=0.93 ᴍᴍ

ʜᴇɴᴄᴇ ʀᴇǫᴜɪʀᴇᴅ ʀᴀᴅɪᴜs ᴏғ ɪᴍᴀɢᴇ ᴏғ sᴜɴ ɪs 0.93ᴍᴍ