Question

determine how far an object must be placed in front of a converging lens of focal length 10 centimetre in order to produce An erect image of linear magnification 4
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Answer 1

Answer:

Explanation:

Given,

Focal length, f = 10 cm

Magnification, m = + 4

To Find,

Object distance, u = ?

Formula to be used,

Magnification formula, i.e m = v/u

Lens formula, i.e 1/v - 1/u = 1/f

Solution,

Putting all the values, we get

m = v/u

⇒ 4 = v/u

⇒ v = 4u ... (i)

Now, we know that,

1/v - 1/u = 1/f

⇒ 1/4u - 1/u = 1/10  [From Eq (i)]

⇒ - 3/4u = 1/10

⇒ u = - 30/4

⇒ u = - 7.5 cm

Hence, the object placed at a distance of 7.5 cm from the lens.

Answer 2

Answer:

Given :-

• A converging lens of focal length is 10 cm in order to produce. An erect image of linear magnification is 4.

To Find :-

• How far an object must be placed in front of the converging lens.

Formula Used :-

❶To find image distance we know that,

✪ m = v/u ✪

where,

• m = Magnification
• v = Image distance
• u = Object distance

❷ To find object we know that,

✯ 1/v - 1/u = 1/f ✯

where,

• v = Image distance
• u = Object distance
• f = Focal length

Solution :-

❶ First, we have to find the image distance,

Given :

• Magnification = 4

According to the question by using the formula we get,

⇒ m = v/u

⇒ 4 = v/u

➠ v = 4u

Hence, the image distance is 4u .

❷ Now, we have to find the object distance,

Given :

• Focal length = 10 cm
• Image distance = 4u

According to the question by using the formula we get,

↦ 1/v -1/u = 1/f

↦ 1/4u - 1/u = 1/10

↦ - 3/4u = 1/10

↦ 4u = - 3 × 10

↦ 4u = - 30

↦ u = - 30/4

➦ u = - 7.5 cm

∴ The object must must be placed in front of a converging lens is - 7.5 cm .