Question

Question 13 20 pts An object is placed 25 cm in front of a lens of focal length 20 cm. 60 cm past the first lens is a second lens of focal length 25 cm. (a) How far past the 25 cm lens does the final image form? (b) What is the ratio of the object height to the image height? (c) Drawing the Ray Diagram to show how the first image and second image is formed using the 3 rays. Make sure you write down the answers to a) an b) in the text entry field before you upload your worksheet. Box your answers in your worksheet. in .HTML Editora BIU A - A - Ix E 1 1 1 x - NVX 60 V D 12pt

Answer 1

Answer -

GIven,

Object Distance = 25 cm

Focal Length of Lens 1 = 20 cm

Distance between Lenses = 60 cm

Focal length of Lens 2 = 25 cm

a) Distance of FInal Image from lens 2 (Focal Length 25 cm) = ?

First,

find the position of Image formed by lens 1

We know that,

1/f = 1/O + 1/I

where,

f = focal length

O = Object distance

I = Image Distance

So,

1/20 = 1/25 + 1/I

0.05 = 0.04 + 1/I

1/I = 0.05 - 0.04

1/I = 0.01

I1 = 100 cm towards the right of the lens 1

We know that,

The distance between the lenses is 60 cm and the image distance from the lens 1 is 100 cm So, the image is formed at a 40 cm distance post the lens 2.

This Image will act as Object for Lens 2 and distance is Negative,

So,

1/f = 1/O + 1/I

1/25 = 1/ (-40) + 1/I

0.04 = -0.025 + 1/I

1/I = 0.04 + 0.025

1/I = 0.065

I = 15.38 cm post the Lens 2 [ANSWER]

b) Ratio of the Object height to the image height = ?

We know that,

Object Height / Image Height = Object Distance / Image Distance

From the above answer,

Object distance from lens 1 = 25 cm

Image distance from lens 1 = 100 cm

So, for Lens 1 ,

Object Height 1  / Image Height 1 = 1/4 --------1

Object distance from lens 2 = 40 cm

Image distance from lens 2 = 15.38 cm

So, for Lens 2 ,

Object Height 2 / Image Height 2 = 40/15.38 --------2

Also, image of lens 1 is acting object for lens 2 So, Height of both are equal. i.e Image Height 1 = Object Height 2.

So,

Object Height 1 / (40/15.38 * Image Height 2)= 1/4

Object Height 1 / Image Height 2)= 1/4 * 40/15.38

Object Height 1 / Image Height 2 = 1/1.54 [ANSWER]

c)

I, za Object X -25cm -focm