PRELIMINARY STAGE 2024
Contest 19
St. Peter’s SHS: 65 points (Winner)
Hohoe E. P. SHS: 44 points
Sirigu Integrated SHS: 07 points
Contest 20
University Practice SHS: 39 points (Winner)
Afua Kobi Ampem Girls’ SHS: 35 points
St. Andrews SHS: 28 points
Contest 21
Apam SHS: 38 points (Winner)
E. PC. Mawuko Girls’ SHS: 31 points
Obiri Yeboah SHTS: 25 points
ROUND 4 - TRUE OR FALSE
QUESTION
The optical power of a lens is measured in diopters.
ANSWER: TRUE
EXPLANATION:
By definition, optical power ($P$) is the reciprocal of the focal length measured in meters:
$P = \dfrac{1}{f}$
$\text{The standard SI unit for this refractive measurement is the diopter (D), where 1 D = 1 m}^{-1}\text{.}$
QUESTION
The numerical value of the optical power of a lens is always greater than unity.
ANSWER: FALSE
EXPLANATION:
$P = \dfrac{1}{f}$
$\text{The optical power of a lens will be less than 1 diopter whenever its focal length is greater than 1 meter.}$
$\text{For example, a flat or weak lens with a focal length of 2 meters has a power of only } 0.5\text{ D.}$
QUESTION
The optical power of a lens of focal length one centimeter is one diopter.
ANSWER: FALSE
EXPLANATION:
$f = 1\text{ cm}$
$f = 1 \times 10^{-2}\text{ m}$
$P = \dfrac{1}{f}$
$P = \dfrac{1}{1 \times 10^{-2}}\text{ D}$
$P = 1 \times 10^{2}\text{ D}$
$P = 100\text{ D}$
$\text{A lens with a focal length of 1 cm has an optical power of 100 diopters, not 1 diopter.}$
---
PRACTICE QUESTIONS
1. QUESTION: A lens of focal length 0.25 m has a power of 4.0 D.
ANSWER: TRUE
EXPLANATION:
$P = \dfrac{1}{0.25}$.
2. QUESTION: A diverging lens has a negative power.
ANSWER: TRUE
EXPLANATION:
Its focal length is negative.
3. QUESTION: A lens of focal length 2.0 m has a power of 2.0 D.
ANSWER: FALSE
EXPLANATION:
$P = 0.50$ D.
4. QUESTION: The power of a lens is found from its focal length in centimetres.
ANSWER: FALSE
EXPLANATION:
The focal length must be in metres.
5. QUESTION: A more strongly curved lens usually has a greater power.
ANSWER: TRUE
EXPLANATION:
It bends light more, so its focal length is shorter.
6. QUESTION: One dioptre equals one metre.
ANSWER: FALSE
EXPLANATION:
It equals one inverse metre.
7. QUESTION: The powers of thin lenses in contact add.
ANSWER: TRUE
EXPLANATION:
$P = P_1 + P_2$.
8. QUESTION: A flat sheet of glass has infinite power.
ANSWER: FALSE
EXPLANATION:
Its focal length is infinite, so its power is zero.
9. QUESTION: A −2.0 D lens has a focal length of −0.50 m.
ANSWER: TRUE
EXPLANATION:
$f = \dfrac{1}{P}$.