An object is placed `30 cm ` to the left of a diverging lens whose focal length is of magnitude `20 cm`. Which one of the following correctly states the nature and position of the virtual image formed ?

Options

A. Nature of image`=` inverted, enlarged , distance form lens`=60cm` to the right
B. Nature of image `=` erect , diminished , distance form lens`= 12 cm` to the left
C. Nature of image `=` inverted, enlarged , distance form lens`= 60 cm` to the left
D. Nature of image `=` erect, diminished, distance form lens`=12 cm` to the right

Answer

B

Explanation

When an object is placed between `2f` and `f(` focal length `)` of the diverging lens, the image is virtual, erect and diminished as shown in the graph. To compute the distance of the image from the lens, we apply
`(1)/(f)=(1)/( v)-(1)/(u)implies(1)/(-2)=(1)/(v)-(1)/(30)`
`implies v=-((20)(30))/(20+30)`
`=-12 cm` ( to the left of the diverging lens.)