Optics Questions and Answers

Answer: B

The gauge pressure is \(78.4 \times 10^{3}\) Pa.

The apparent depth is the real depth divided by the refractive index, so the real depth is \(6 \times \frac{4}{3} = 8\) m.

\[ \begin{aligned} p &= h\rho g = 8 \times 1000 \times 9.8 \\ &= 78.4 \times 10^{3}\ \text{Pa} \end{aligned} \]

Using the apparent depth 6 m gives \(58.8 \times 10^{3}\) Pa, and dividing by \(\frac{4}{3}\) instead of multiplying gives \(4.5\) m and about \(44 \times 10^{3}\) Pa.

Answer: A

The image is at -30 cm.

A power of +5 D means a converging lens of focal length \(f = \frac{100}{5} = 20\) cm. With the object at u = -12 cm (inside the focal length):

\[ \begin{aligned} \frac{1}{v} &= \frac{1}{f} + \frac{1}{u} = \frac{1}{20} - \frac{1}{12} \\ &= -\frac{1}{30} \Rightarrow v = -30\ \text{cm} \end{aligned} \]

The negative sign means a virtual image on the same side as the object, as a magnifying glass gives. 20 cm is the focal length itself, and -12 cm is the object distance, not the image distance.

Answer: E

The ratio is 16 : 1.

Intensity is proportional to the square of the amplitude, so the amplitudes are in the ratio \(\sqrt{25} : \sqrt{9} = 5 : 3\).

\[ \begin{aligned} \frac{I_{max}}{I_{min}} &= \frac{(5 + 3)^{2}}{(5 - 3)^{2}} \\ &= \frac{64}{4} = 16 \end{aligned} \]

5 : 3 is the amplitude ratio, and 9 : 1 or 16 : 3 come from squaring only part of the expression. The minimum is not zero because the two waves have unequal amplitudes, so they never cancel completely.

Answer: C

Light waves are similar in nature to gamma rays.

Visible light and gamma rays are both electromagnetic waves: oscillating electric and magnetic fields travelling at the speed of light. They differ only in wavelength, gamma rays being at the short-wavelength, high-energy end of the spectrum.

Cathode rays are streams of electrons, alpha rays are helium nuclei, and cosmic rays are mostly high-energy protons and atomic nuclei. These are particles, not electromagnetic waves.

Answer: D

The wrong statement is Light cannot travel through vacuum.

Light is an electromagnetic wave and needs no medium; it travels fastest in a vacuum, at about \(3 \times 10^{8}\) m/s, which is how sunlight reaches the earth across empty space.

The other three statements are true. Light travels in straight lines in a uniform medium (hence sharp shadows), it is a wave motion, and its speed is vastly greater than that of sound, about 340 m/s in air, which is why lightning is seen before thunder is heard.

Answer: C

A dental surgeon uses a concave mirror.

When an object, here a tooth, is placed between a concave mirror and its focus, the mirror forms an enlarged, erect, virtual image. The dentist therefore sees a magnified view of the tooth, and the mirror also concentrates light on it.

A plane mirror gives an image of the same size, and a convex mirror gives a diminished image (useful for the wide field of a rear-view mirror), so neither magnifies the tooth.

Answer: C

The images are magnified, real and inverted in case (i), and magnified, virtual and erect in case (ii).

The focal length of the mirror is \(f = R/2 = 7.5\) cm, and its centre of curvature is at 15 cm.

(i) At 10 cm the object is between F and C (7.5 cm and 15 cm), so the image forms beyond C and is real, inverted and magnified. (ii) At 5 cm the object is between the pole and F, so the image is virtual, erect and magnified, as in a shaving mirror.

The options giving the same nature in both cases ignore that the object crosses the focus, and the last option pairs 'real' with 'erect', which a concave mirror never gives for a real object.

Answer: D

The Cassegrain telescope provides a large focal length in a short telescope.

In a Cassegrain reflector, light from the concave primary mirror is reflected back by a convex secondary mirror through a hole in the primary. The convex secondary increases the effective focal length, while folding the light path keeps the tube short. A long focal length gives high magnification without a very long instrument.

The options with a short focal length reverse the advantage, and 'large focal length in large telescope' misses the point that the design keeps the tube compact.

Answer: A

The lateral magnification is +0.44.

For a convex mirror with R = 22 cm, the focal length is f = +11 cm. With the object in front, u = -14 cm (New Cartesian convention):

\[ \begin{aligned} \frac{1}{v} &= \frac{1}{f} - \frac{1}{u} = \frac{1}{11} + \frac{1}{14} \\ &= \frac{25}{154} \\ v &= +6.16\ \text{cm} \end{aligned} \]

\[ m = -\frac{v}{u} = -\frac{6.16}{-14} = +0.44 \]

The positive sign shows an erect, virtual image, as a convex mirror always gives; -0.44 has the wrong sign for a convex mirror.

Answer: C

The wavelength in glass is about 416 nm.

When light enters a medium of refractive index n, its frequency stays the same but its speed and wavelength are divided by n:

\[ \begin{aligned} \lambda_{glass} &= \frac{\lambda_0}{n} = \frac{632}{1.52} \\ &= 415.8\ \text{nm} \end{aligned} \]

The angle of incidence and the thickness of the slide do not affect the wavelength inside the glass; they are extra data. 632 nm would mean no change, and 961 nm is what you get by multiplying by n instead of dividing.