Question

An object 4cm in size is placed at 20cm from a convex mirror of focal length 30cm . Find the position nature &size of the image

Answer 1

GiveN :

• Object Height (Ho) = 4 cm
• Object Distance (u) = -20 cm
• Focal length (f) = 30 cm
• Convex Mirror

To FinD :

• Position, Size and Nature of image

SolutioN :

Use mirror formula :

⇒1/f = 1/v + 1/u

⇒1/v = 1/f - 1/u

⇒1/v = 1/30 - (-1/20)

⇒1/v = 1/30 + 1/20

⇒1/v = (2 + 3)/60

⇒1/v = 5/60

⇒v = 60/5

⇒v = 12

$\therefore$ Image is placed at a distance of 12 cm from mirror.

________________________

Now, use formula for magnification :

⇒m = -v/u = H'/Ho

⇒-12/-20 = H'/4

⇒12/20 = H'/4

⇒H' = (12 * 4)/20

⇒H' = 12/5

⇒H' = 2.4

• Image height is 2.4 cm
• Nature of Image is Virtual and erect

Answer 2

Given,

size of object , H₀ = 4 cm

object distance , u = -20 cm

focal length of concave mirror , f = 30 cm

Use formula ,

1/v + 1/u = 1/f

⇒1/v + 1/-20 = 1/30

⇒1/v = 1/30 - (-1/20) = (2 + 3)/60 = 5/60 cm

⇒ v = 12 cm

∴ image is formed object side , 12 cm from pole of concave mirror.

Now, use formula,

Hi/H₀ = -v/u

Where Hi is the size of image .

Now, Hi/4 cm = -12/(-20cm)

Hi = -4 × 12/20 cm = 2.4 cm

∴ size of image = 2.4 cm

Hence, object should place 12 cm left side of mirror and size of image is 2.4 cm .it is inverted and larger than object's size.

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