Question

A object is place at distance of 0.30 m from a convex lens of focal length 0.15 m find the size of an object when a size of the image is 0.01m

Answer 1

Given:-

• Object distance, u = 0.30m = -30cm

• Focal length ,f = 0.15m = 15cm

• Image - height ,hi = 0.01m = 1 cm

To Find:-

• Size of object, ho

Solution:-

Firstly we calculate the image distance

Using lens Formula

• 1/v - 1/u = 1/f

Substitute the value we get

→ 1/v -1/(-30) = 1/15

→ 1/v + 1/30 = 1/15

→ 1/v = 1/15-1/30

→ 1/v = 2 -1/30

→ 1/v = 1/30

→ v = 30cm

Therefore, the image distance is 30cm.

Now, Using magnification Formula

• m = hi/ho = v/u

Substitute the value we get

→ hi/ho = v/u

→ 1/ho = 30/(-30)

→ 1/ho = -1

→ ho = -1/1

→ ho = -1

Therefore, the height of the object is 1 cm

Negative sign show that the image formed is real and Inverted and the image height is equal to the object height.

Answer 2

Given :-

Type of lens :- Convex lens

• Object distance (u) = 0.30 m ⟹ 0.30 × 100 ⟹ -30 cm
• Focal length (f) = 0.15 m ⟹ 0.15 × 100 ⟹ 15 cm
• Size of the image (hi) = 0.01 ⟹ 0.01 × 100 ⟹ 1 cm

To Find :-

• Size of object (ho).

Solution :-

Case (I), The image distance,

Applying lens formula,

★ 1/v - 1/u = 1/f

[ Put the values ]

⟹ 1/v - 1/(-30) = 1/15

⟹ 1/v + 1/30 = 1/15

⟹ 1/v = 1/15 - 1/30

⟹ 1/v = 2-1/30

⟹ 1/v = 1/30

⟹ v = 30 cm ★

Case (II), Size of object,

Applying magnification formula,

★ m = hi/ho = v/u

[ Put the values ]

⟹ hi/ho = v/u

⟹ 1/ho = 30/-30

⟹ 1/ho = -1

⟹ ho = -1/1

⟹ ho = -1 cm ★

[ Note :- Negative sign indicates the image formed is real and inverted and image height = object height ]

Hence solved !!