Question

Constants A bright object and a viewing screen are separated by a distance of 82.5 cm. Part A At what distance(s) from the object should a lens of focal length 16.5 cm be placed between the object and the screen in order to produce a crisp image on the screen? Express your answer using three significant figures. If there is more than one answer, enter your answers in ascending order separated by commas. VALO ? d = cm from the object Submit Request Answer

Answer 1

Distance between object and viewing screen (u + v )= 82.5cm

            Focal length of lens f = 16.5cm

Location of lens between object and the screen

            u + v = 82.5cm

            u = 82.5- v -----------(1)

From the lens formula-

⇒   1/u + 1/v = 1/f

⇒ v + u/ uv = 1/f

Subtituting the value of u from ....(1)

(v + 82.5- v) / (82.5- v)v = 1/f

82.5 / (82.5v - v²) = 1 / 16

1361.25 = 82.5v - v²

v² - 82.5v + 1361.25 = 0

By solving the quadratic equation

v = 22.8cm, or 59.69cm

Therefore, the lens should be placed at a distance of 22.8cm between the object and the screen