Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q101P

Expert-verified
Fundamentals Of Physics
Found in: Page 1043

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

The formula 1p+1i=1f is called the Gaussian form of the thin-lens formula. Another form of this formula, the Newtonian form, is obtained by considering the distance x from the object to the first focal point and the distance x' from the second focal point to the image. Show that xx'=f2 is the Newtonian form of the thin-lens formula

The Newtonian form of the thin-lens formula is xx'=f2.

See the step by step solution

Step by Step Solution

Step 1: Given data

  • Distance from the object to the first focal point = x.
  • Distance from the second focal point to the image role="math" localid="1663015192526" = x'.

Step 2: Understanding the concept of thin-lens formula

In the given problem, we have to convert the Gaussian form of the thin-lens formula to the Newtonian form. So first we find the object's distance. The value of x is dependent on the position of the object. After that, we find the image distance where the value of x’ is dependent on the position of the image formed. We consider x and x’ as positive, i.e., the object is outside the focal point and the image is outside the focal point. Now by using the Gaussian formula, we solve for i and substituting the object distance and image distance, we prove the Newtonian form.

Formula:

The lens formula,

1f=1p+1i ...(i)

Step 3: Calculation of the Newtonian thin-lens formula

Let, the object distance be p = f + x and the image distance be i = f + x', where, f is the focal length, p is the object distance, and i is the image distance.

And x is the distance from the object to the first focal point, x' is distance from the second focal point to the image.

Now, from equation (i), we get that the image distance as follows:

1i=1f-1p1i=p-fpf

so,

i=fpp-f ...(1)

By substituting the value of p = f + x in the equation (1), we get the above equation as follows:

i=ff+x f+x -f =ff+x x

As,

i = f + x'

f+x'=ff+x x x'=ff+x x -f x'=f2+fx-fxx x'=f2x xx'=f2

Hence, the thin-lens formula is xx'=f2.

Most popular questions for Physics Textbooks

Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.