Question 82: Ray Optics

Question

Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance $(u)$ and image distance (v) using same convex lens having power +5 D as $(25,96),(30,62),(35,37),(45,35)$ and $(50,32)$ respectively. Identify correct statement

Accepted Answer

The power $(\mathrm{P})$ of the lens is given as +5 D .
The relationship between power and focal length (f) in meters is $\mathrm{P}=\frac{1}{\mathrm{f}}$.
$$ \mathrm{f}=\frac{1}{\mathrm{P}}=\frac{1}{5} \mathrm{~m}=20 \mathrm{~cm} $$
For a convex lens forming a real image, the lens formula is:
$$ \frac{1}{f}=\frac{1}{v}-\frac{1}{u} $$
Using sign convention for a real object ( $u$ is negative) and a real image ( $v$ is positive):
$$ \frac{1}{20}=\frac{1}{v}-\frac{1}{-u} \Rightarrow \frac{1}{20}=\frac{1}{v}+\frac{1}{u} $$
The theoretical image distance $\left(\mathrm{v}_{	ext {th }}ight)$ for each person can be determined for given object distance $(\mathrm{u})$ using $\mathrm{v}_{	ext {th }}=\frac{\mathrm{uf}}{\mathrm{u}-\mathrm{f}}$ (where u is the magnitude).
For person $\mathrm{P}_1$ the object distance
Person
u
v
th
Measured v
Absolute Error
P
1
(25,96)
25
25 ÃÂ 20
25 Ã¢ÂÂ 20
= 100 cm
96
|100 Ã¢ÂÂ 96| = 4 cm
P
2
(30,62)
30
30 ÃÂ 20
30 Ã¢ÂÂ 20
= 60 cm
62
|60 Ã¢ÂÂ 62| = 2 cm
P
3
(35,37)
35
35 ÃÂ 20
35 Ã¢ÂÂ 20
= 46.6 cm
37
|46.6 Ã¢ÂÂ 37| = 9.6 cm
P
4
(45,35)
45
45 ÃÂ 20
45 Ã¢ÂÂ 20
= 36 cm
35
|36 Ã¢ÂÂ 35| = 1 cm
P
5
(50,32)
50
50 ÃÂ 20
50 Ã¢ÂÂ 20
= 33.3 cm
32
|33.3 Ã¢ÂÂ 32| = 1.3 cm
Most readings have slight experimental errors (within 2-4 cm). However, for Person $\mathrm{P}_3$, the recorded value of 37 cm is significantly different from the theoretical value of 46.6 cm (an error of 9.6 cm ). This makes $\mathrm{P}_3$ 's reading distinctly incorrect compared to the others.
Therefore, the data recorded by person $P_3$ is mathematically inconsistent with the properties of a lens with 20 cm focal length.
Hence, the correct option is (C).

Answer

Readings recorded by $P_3$ and $P_2$ persons are incorrect

Answer

Readings recorded by all persons are correct

Answer

Readings recorded by $P_3$ person are incorrect

Answer

Readings recorded by $P_4$ and $P_5$ persons are incorrect

Ray Optics

Five persons P_1, P_2, P_3, P_4 and P_5 recorded object distance (u) and image distance (v) using same convex lens having power +5 D as (25,96),(30,62),(35,37),(45,35) and (50,32) respectively. Identify correct statement

Choose the correct answer: