Question

a needle placed 45 cm from a lens forms an image on the screen at 90 cm. identify the type of the lens. determine the focal length and power and what is the size of the image if the needle is 5 cm height. Draw the ray diagram

Answer 1

Since Image is formed at screen it is a real and inverted image thus

Object distance = u = -45 cm

Image distance =  v = 90 cm

Now since image is magnified thus it is a convex lens

As per the lens formula,

1/f = 1/v - 1/u

∴ 1/f = 1/90 - ( -1/45) = 1/90 + 1/45

Solving it we get focal length = +30cm = 0.3 m

Power = 1/f = 1/0.3 = 3.33 D

Now, Magnification = v/u = 90/-45 = -2

Also, Magnification = Height of Image / Height of Object

Thus, Height of Image/ 5 = -2

Solving which we get, Height of Image = -10 cm

Showing that image is real and inverted