Question

A point object is kept 10cm away from one of the surface of a thick double convex lens of refractive index 1.5 and radius of curvature 10 cm and 8cm. Central thickness of the lens is 2 cm. determine location of the final image considering paraxial only

Answer 1

Hi,

Answer:

The location of the final image is 120 cm.

Explanation:

Given data:

In a double convex lens,

Object distance, u = -10 cm

Refractive index, n = 1.5

Radius of curvatures, R1 = 10 cm and R2 = -8 cm

Central thickness of the lens, t = 2 cm

To find: final image distance, “v” considering paraxial only

For thick convex lens, we have

Focal length, f is positive

R1 is positive

R2 is negative

Object distance “u” is negative and image distance “v” is positive

Image formed is real & inverted

We know, the lens maker’s formula is given as  

$\frac{1}{f}$ = [n-1][$\frac{1}{R1}$ – $\frac{1}{R2}$ + $\frac{(n - 1) * t}{nR1R2}$]

Or, $\frac{1}{f}$ = [1.5-1][(1/10) + (1/8) - {(1.5 - 1)*2 / (1.5 * 10 * 8)}]

Or, $\frac{1}{f}$  = [0.5] [0.1 + 0.125 – (1/120)]

Or, $\frac{1}{f}$  = [0.5] [0.21667] = 0.108335

Now, as per the general lens formula, we have

$\frac{1}{f}$ = $\frac{1}{v}$ – $\frac{1}{u}$

Or, 0.108335 = 1/v – 1/(-10)

Or, 0.108335 – 0.1 = 1/v

Or, $\frac{1}{v}$  = 0.008335

∴ v = 1/0.008335 = 119.97 cm ≈ 120cm

Hence, the location of the final image is 120 cm away from the lens considering paraxial only.

Hope this helps!!!!!

Answer 2

Answer:

The location of the final image is 120 cm.

Explanation:

Given data:

In a double convex lens,

Object distance, u = -10 cm

Refractive index, n = 1.5

Radius of curvatures, R1 = 10 cm and R2 = -8 cm

Central thickness of the lens, t = 2 cm

To find: final image distance, “v” considering paraxial only

For thick convex lens, we have

Focal length, f is positive

R1 is positive

R2 is negative

Object distance “u” is negative and image distance “v” is positive

Image formed is real & inverted

We know, the lens maker’s formula is given as  

= [n-1][ –  + ]

Or,  = [1.5-1][(1/10) + (1/8) - {(1.5 - 1)*2 / (1.5 * 10 * 8)}]

Or,   = [0.5] [0.1 + 0.125 – (1/120)]

Or,   = [0.5] [0.21667] = 0.108335

Now, as per the general lens formula, we have

=  –

Or, 0.108335 = 1/v – 1/(-10)

Or, 0.108335 – 0.1 = 1/v

Or,   = 0.008335

∴ v = 1/0.008335 = 119.97 cm ≈ 120cm

Hence, the location of the final image is 120 cm away from the lens considering paraxial only.

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Explanation: