Question

An object is placed in front of a convex lens with a focal length, f of 10 cm. What are the characteristics of the image formed if the object distance is 15 cm?​

Answer 1

Question:

• An object is placed in front of a convex lens with a focal length, f of 10 cm. What are the characteristics of the image formed if the object distance is 15 cm?

Information provided with us:

• Focal length at which object is placed is of 10cm
• Object distance is 15 cm

What does we have to calculate:

• We have to calculate the image distance and the nature of image formed.

Remember that,

• Object distance is u
• focal length is f

Formula needs to be used:

Lens Formula:-

• 1/v - 1/u = 1/f

Also remember that u is negative.

Linear magnification:-

• m = length of image (I) / length of object (O)

Or,

• m = v/u

Evaluating the values,

• Here we are evaluating the values in the first formula which is lens formula.

=> 1/v - 1/-15 = 1/10

• We know that, by multiplying minus sign with minus sign we gets plus.

=> 1/v + 1/15 = 1/10

• Transposing 1/15 from L.H.S. to R.H.S. it would be negative.

=> 1/v = 1/10 - 1/15

• Taking L.C.M.,

=> 1/v = (1×3 / 10×3) - (1×2 / 15×2)

=> 1/v = 3/30 - 2/30

=> 1/v = (3-2/30)

• On subtracting 3 with 2 we gets 1,

=> 1/v = 1/30

• On cross multiplying,

=> v = 30

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• Here we are evaluating the values in the above given second formula of linear magnification,

=> m = 30/15

• Cancelling by 5,

=> m = 6/3

• Cancelling by 3,

=> m = 2

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• Characteristics of image is inverted and real and distance of image is of 30 cm