Question

an object 60cm from a lens gives a virtual image at a distance of 20cm in front of the lens what is the focal length of the lens?is the lens converging or diverging.

Answer 1

Given,
Onject distance, u = - 60 cm
image distance, v = - 20 cm
Focal length, f = ?


Now, using the lens formula,
1/f = 1/v - 1/u
= 1/(-20) - 1/ (-60)
= 1/60 - 1/20
= 1 - 3 / 60
= - 2/ 60

i.e., focal length, f = - 30 cm
Hence, the lens is a diverging less with focal length of 30 cm.
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Answer 2

The focal length is one of the most important parameter of a lens.

Sometimes the focal length is slightly different from the datasheet value given by the manufacturer, having an impact on the predicted optical system performances.

                                            \frac {1}{f} = \frac{1}{ v} - \frac{1}{u}  

                                             = \frac{1}{ -20} - \frac {1} {-60}

                                             = \frac {-2 }{60}  

                                             f = -30 .

Since focal length is negative so it is diverging lense.