Question

An equiconvex lens is cut into two equal parts along a plane perpendicular to the principal axis. If the power of the original lens is 4D, the power of one of the two parts is

Answer 1

Answer:

$Power =2D$

Explanation:

Hey there!!

We need to make use of LENS-MAKERS formula to solve this sum

Lens-makers formula:

$\boxed{\frac{1}{f}=(\frac{\mu_2}{\mu_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})}$

Where  $\mu_2 :$ R.I of lens medium

            $\mu_1 :$ R.I of surrounding medium, in this case Air

According to this equation,

$Power=4=(\mu_2-1)(\frac{1}{R}-\frac{1}{-R})\\\\=> 4 = (\mu_2-1)(\frac{2}{R})\\\\=> \boxed{2 = \frac{(\mu_2-1)}{R}}----(1)$

When the lens is cut, it gives two identical parts as shown in the figure.

Of the two surfaces, the radii of curvature of one remains R and of the other becomes ∞.

So now applying lens makers formula for this one, we get

$Power= (\mu_2-1)(\frac{1}{R}-\frac{1}{infinity})\\\\=>\boxed{P'= \frac{(\mu_2-1)}{R}}----(2)$

From (1) and (2), we get that power of the pieces are 2D

Hope this answer helped you :)

Answer 2

The power of lens is 3 D.

Explanation:

We are given that:

The power of original lens = 4 D

To Find: The power of one of teh two parts = ?

Solution:

By using lens maker formula.

1 / f = ( n - 1 ) [ 1 / R1 - 1 / R2 ]

• f is the focal length
• n is the refractive index
• R1 is the radius of curvature of sphere 1
• R2 is the radius of curvature of sphere 2

Now

P = P2 + P1

4 D = P2 + 2 D

P2 = 4 D - 2 D

P2 = 2 D

P = P2 + P1

4 D = P2 + D

P2 = 4 D - D

P2 = 3 D

Thus the power of lens is 3 D.