Question

An object is 17.4 cm to the left of a lens with a focal length of 12.4 cm. A second lens of focal length 14.7 cm is 54.91 cm to the right of the first lens. The height of the object of is 3.6 cm.

What is the location of the final image with respect to the second lens?
What is the height of the image?

Also determine is the image real or virtual and, with respect to the original object, upright or inverted? Check all statements that are true.

The image is inverted
The image is virtual
The image is upright
The image is real

Answer 1

Given,

o1 = 17.4 cm ; f1 = 12.4 cm ; f2 = 14.7 cm ; D = 54.91 cm ; ho = 3.6 cm

We know from lens eqn

1/f = 1/i + 1/o

i = o x f/(o - f)

i1 = 17.4 x 12.4/(17.4 - 12.4) = 43.15 cm

o2 = D - i1

o2 = 54.91 - 43.15 = 11.76 cm

i2 = 11.76 x 14.7/(11.76 - 14.7) = -58.8 cm

Hence, i2 = -58.8 cm

we know that

M = -i/o

m1 = -43.15/14.7 = -2.48

m2 = -(-58.8)/11.76 = 5

M = m1 m2 = -2.48 x 5 = 12.4

h' = 12.4 x 3.6 = 44.64 cm

Hence, h' = 44.64 m

The image is virtual and inverted.