Question

A converging lens has a focal length of 46.0 cm. If an object is at a distance of 13.1 cm from the lens, determine the location d of the image, the magnification m, and the type of image, if it exists. d = -18.4 cm, m = 1.4, virtual and upright d = +18.4 cm, m = -1.4, real and inverted image does not exist d = 56.2 cm, m = -0.222, real and inverted d = -23.0 cm, m = 1.4, virtual and upright

Answer 1

Focal length of the converging lens = f = 46 cm.

Object distance = u = - 13.1 cm.

Hence, image distance d is given by :

1 / f = 1 / d - 1 / u

or, 1 / d = 1 / f + 1 / u = ( u + f ) / uf

or, d = uf / ( u + f ) = { ( - 13.1 ) x 46 / ( - 13.1 + 46 ) } cm ~ - 18.4 cm.

Hence, magnification = m = d / u = - 18.4 cm / - 13.1 cm ~ + 1.4.

Since, both u and d are negative, the image is virtual.

Since, m is positive, the image is upright.

Hence, correct option is : d = - 18.4 cm, m = 1.4, virtual and upright.