Question

What is the focal length of the eye-lens system when viewing an object at infinity? Assume that the lens-retina distance is 2.0 cm . Follow the sign conventions. Express your answer using two significant figures and include the appropriate units.

Answer 1

Answer:

Focal length of the eye-lens is 2.0 cm

Explanation:

Given:

An eye-lens system which will follow converging lens (convex lens) sign conventions and knowing that lens-retina distance is the image distance.

Object distance, $u$ = $-\infty$

Image distance, $v$ = $2.0$ cm

We have to find the focal length.

Lets say that the focal length is $f$ .

Lens Formula:

⇒ $\frac{1}{f} =\frac{1}{-u} +\frac{1}{v}$

Sign-convention:

We will follow the Cartesian coordinate,placing the lens at the origin of the plane, optical center is at $(0,0)$ now as the object will be towards negative x-axis so it is negative others are on the right side of the origin so they are positive.

Using the lens formula:

⇒ $\frac{1}{f} =\frac{1}{-u} +\frac{1}{v}$

⇒ $\frac{1}{f} =\frac{1}{-\infty} +\frac{1}{2.0}$      

⇒ $\frac{1}{f} =0+\frac{1}{2.0}$         ...as $\frac{1}{\infty}=0$ and there is no $-0$ so it is zero only.

⇒ $f=2.0$ cm

So the focal length is 2.0 cm with two significant figures.