Question

How far should one hold an object from a concave mirror of focal length 40 cm so as to get an image twice the size of the object

Answer 1

Answer:

How far should we hold an object from a concave mirrow of focal length 40cm so as to get a virtual image twice the size of the object?

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How far should we hold an object from a concave mirrow of focal length 40cm so as to get a virtual image twice the size of the object?

It’s the shaving-mirror situation, so expect an answer less than f, less than 40 cm

Let the object distance be u then the image distance v is -2u

2u because the magnification is 2, minus because it is a virtual distance, to a virtual image, behind the mirror. Also it’s an upright image; inverted images have negative magnification.

apply lens formula: 1/u + 1/v = 1/f

1/u + (1/-2u) = 1/40

1/u - 1/2u = 1/40

1/2u = 1/40

2u = 40

u = 20

Object is 20 cm in front of mirror.

Answer 2

Answer:

It’s the shaving-mirror situation, so expect an answer less than f, less than 40 cm

Let the object distance be u then the image distance v is -2u

2u because the magnification is 2, minus because it is a virtual distance, to a virtual image, behind the mirror. Also it’s an upright image; inverted images have negative magnification.

apply lens formula: 1/u + 1/v = 1/f

1/u + (1/-2u) = 1/40

1/u - 1/2u = 1/40

1/2u = 1/40

2u = 40

u = 20

Object is 20 cm in front of mirror.

Hope this may help you.