IMO Practice Test — The Human Eye and the Colourful World
12 Questions • 15 min • Olympiad level
15:00
Question 1 of 12
medium
A myopic person has a far point of 2 m. The power of the corrective lens is
-0.5 D
+0.5 D
-2 D
+2 D
Explanation: f = -2 m, P = 1/f = -0.5 D (concave lens).
Question 2 of 12
hard
A hypermetropic eye has a near point of 50 cm. The power of the lens to read at 25 cm is
+2 D
-2 D
+4 D
+1 D
Explanation: u = -0.25 m, v = -0.5 m; 1/f = 1/-0.5 - 1/-0.25 = -2 + 4 = 2; P = +2 D.
Question 3 of 12
medium
If a lens has power +5 D, its focal length is
5 cm
50 cm
2 cm
20 cm
Explanation: f = 1/P = 1/5 = 0.2 m = 20 cm.
Question 4 of 12
hard
Two thin lenses of powers +3 D and -1 D are placed in contact. The net power is
+2 D
+4 D
-2 D
+3 D
Explanation: Powers add in contact: 3 + (-1) = +2 D.
Question 5 of 12
hard
Through a prism, which colour travels with the highest speed inside the glass?
violet
green
all the same
red
Explanation: Red bends least, so glass has the lowest refractive index for red — highest speed.
Question 6 of 12
medium
The colour of scattered light by very fine particles is most strongly
red
yellow
green
blue
Explanation: Fine particles scatter shorter (blue) wavelengths the most.
Question 7 of 12
hard
The apparent flattening of the Sun's disc at sunset is due to
dispersion
atmospheric refraction
scattering
diffraction
Explanation: Refraction bends the lower edge more, flattening the disc.
Question 8 of 12
medium
The Sun is visible about 2 minutes before actual sunrise because of
scattering
reflection
dispersion
atmospheric refraction
Explanation: Refraction bends sunlight over the horizon, advancing sunrise.
Question 9 of 12
hard
A person needs a lens of power -1.25 D. The defect and far point are
hypermetropia, 80 cm
myopia, 80 cm
myopia, 125 cm
presbyopia, 80 cm
Explanation: Negative power means myopia; f = 1/-1.25 = -0.8 m, far point 80 cm.
Question 10 of 12
medium
Danger signal lights are red because red light
is scattered the most
is scattered the least
travels slowest in air
has the shortest wavelength
Explanation: Red scatters least, so it travels farthest and is seen from a distance.
Question 11 of 12
medium
Bi-focal lenses are required when a person suffers from
only myopia
only hypermetropia
cataract
both myopia and presbyopia
Explanation: Concave upper part for distance and convex lower part for reading.
Question 12 of 12
hard
An object at infinity is seen clearly by a myopic eye whose far point is 40 cm using a lens of power
-2.5 D
+2.5 D
-4 D
+4 D
Explanation: f = -0.4 m, P = 1/-0.4 = -2.5 D (concave lens).