Question

The size of the image, if an object of 2.5 m height is placed at a distance of 10 cm from a concave mirror is:(Take radius of curvature of concave mirror = 30 cm)

Answer 1

Height of object = h = +2.5 m = 250 cm

Object distance = u = -10cm

R = -30 cm

Focal length = R/2 = -15 cm

Image distance = v = ?

Height of image = h' = ?

Applying mirror formula,

1/f = 1/v + 1/u

1/v = 1/f - 1/u
      =-1/15  + 1/10
     = -2+3/30
     =-1/30

v = -30 cm

We know that ,

magnification = m

m = -v/u
    = -(-30)/-10
   = -3

Also,

m = h'/h
-3 = h'/250
h' = -750 cm

Size of the image = h' = 750 cm 

The image is 750 cm or 7.5 metres high

Answer 2

$\huge\mathfrak{Bonjour!!}$

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

✒ ʜᴇʀᴇ, ɢɪᴠᴇɴ

★ ʜ= 2.5 ᴄᴍ,

★ ᴜ= -10 ᴄᴍ.

ғ = ʀ/2 = -30/2 = -15 ᴄᴍ.

1/ғ = 1/ᴜ + 1/ᴠ

ᴛʜᴇʀᴇғᴏʀᴇ,

- 1/15 = - 1/10 + 1/ᴠ

=> - 1/15 + 1/10 = 1/ᴠ

ᴛʜᴇʀᴇғᴏʀᴇ,

1/ᴠ = -2+3/30 = 1/30

ᴛʜᴇʀᴇғᴏʀᴇ,

ᴠ= 30 ᴄᴍ.

ᴀs, ᴠ ɪs +ᴠᴇ, ᴛʜᴇʀᴇғᴏʀᴇ, ᴛʜᴇ ɪᴍᴀɢᴇ ɪs ᴠɪʀᴛᴜᴀʟ, ᴇʀᴇᴄᴛ ᴀɴᴅ ᴏɴ ᴛʜᴇ ʙᴀᴄᴋ sɪᴅᴇ ᴏғ ᴛʜᴇ ᴍɪʀʀᴏʀ.

★ sɪᴢᴇ : ᴍᴀɢɴɪғɪᴄᴀᴛɪᴏɴ, ᴍ = ʜ'/ʜ = - ᴠ/ᴜ

ʜ' = - ᴠ/ᴜ × ʜ

= -30/-10 × 2.5

= + 7.5 ᴄᴍ.

=> ᴛʜᴇ ɪᴍᴀɢᴇ ɪs ᴠɪʀᴛᴜᴀʟ ᴀɴᴅ ᴍᴀɢɴɪғɪᴇᴅ. ᴛʜᴇ +ᴠᴇ sɪɢɴ sʜᴏᴡs ᴛʜᴀᴛ ᴛʜᴇ ɪᴍᴀɢᴇ ɪs ғᴏʀᴍᴇᴅ ᴀʙᴏᴠᴇ ᴛʜᴇ ᴘʀɪɴᴄɪᴘᴀʟ ᴀxɪs, ɪ.ᴇ., ɪᴛ ɪs ᴠɪʀᴛᴜᴀʟ ᴀɴᴅ ᴇʀᴇᴄᴛ.

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