Optics

The power of a lens of focal length 10 cm is

[amp_mcq option1=”0⋅1 dioptre” option2=”1 dioptre” option3=”10 dioptre” option4=”100 dioptre” correct=”option3″]

The power (P) of a lens is defined as the reciprocal of its focal length (f). The focal length must be expressed in meters for the power to be in dioptres (D).
Given focal length f = 10 cm.
Convert focal length to meters: f = 10 cm / 100 cm/m = 0.1 meters.
Power P = 1 / f (in meters) = 1 / 0.1 m = 10 dioptres.

Power of a lens (in dioptres) = 1 / Focal length (in meters).

A convex lens has a positive focal length and positive power, indicating that it converges light rays. A concave lens has a negative focal length and negative power, indicating that it diverges light rays. The unit dioptre is defined as m⁻¹.

A convex lens has a focal length of 15 cm. At what distance should an object be placed in front of the lens to get a real image of the same size of the object ?

[amp_mcq option1=”15 cm” option2=”10 cm” option3=”30 cm” option4=”40 cm” correct=”option3″]

An object should be placed at a distance of 30 cm from the convex lens.

For a convex lens, a real image of the same size as the object is formed when the object is placed at a distance equal to twice the focal length (2f) from the lens. At this position (often referred to as 2F or C), the image is also formed at a distance of 2f on the opposite side of the lens, and it is real, inverted, and of the same size as the object. Given the focal length (f) is 15 cm, the object distance required is 2 * f = 2 * 15 cm = 30 cm.

Placing the object at the focal length (15 cm) results in an image at infinity. Placing the object between the focal length and the lens results in a virtual, erect, and magnified image. Placing the object beyond 2f results in a real, inverted, and diminished image.

The twinkling of a star is due to :

[amp_mcq option1=”atmospheric reflection of starlight.” option2=”atmospheric refraction of starlight.” option3=”continuous change in the position of the star.” option4=”oscillation of starlight.” correct=”option2″]

The twinkling of a star is due to atmospheric refraction of starlight.

Starlight travels through the Earth’s atmosphere before reaching our eyes. The atmosphere is composed of layers with different densities and temperatures, causing the refractive index to vary continuously. As starlight passes through these varying layers, it is refracted or bent slightly in different directions. This continuous change in the path of light causes fluctuations in the apparent brightness and position of the star, leading to the twinkling effect.

Planets, being much closer, appear as discs rather than point sources of light. Although their light is also refracted, the light from different parts of the disc averages out the effect, which is why planets do not typically twinkle as much as stars. Reflection (bouncing light off a surface) is not the cause of twinkling.

If the magnification produced by a lens is +2, then the image is :

[amp_mcq option1=”erect, virtual and smaller than the object.” option2=”inverted, real and smaller than the object.” option3=”erect, virtual and larger than the object.” option4=”inverted, real and larger than the object.” correct=”option3″]

The magnification produced by a lens is given by the ratio of the image height to the object height (m = h’/h). The sign of the magnification provides information about the nature and orientation of the image.

A positive magnification (+m) indicates that the image is erect (upright) relative to the object. A negative magnification (-m) indicates that the image is inverted. The magnitude of the magnification (|m|) indicates the size of the image relative to the object: |m| > 1 means the image is larger, |m| = 1 means it’s the same size, and |m| < 1 means it's smaller. A magnification of +2 means the image is erect (due to the + sign) and is twice the size of the object (|2| > 1). For a single lens, an erect image is always a virtual image.

Real images formed by a single lens are always inverted, and virtual images are always erect. Therefore, a positive magnification (+2) implies an erect and virtual image that is magnified (larger than the object). This type of image is typically formed by a converging (convex) lens when the object is placed within its focal length.

How many internal reflections of light take place in the formation of primary rainbow ?

[amp_mcq option1=”0″ option2=”1″ option3=”2″ option4=”More than 2″ correct=”option2″]

A primary rainbow is formed when sunlight is dispersed by water droplets. The process involves the sunlight entering a raindrop, undergoing refraction at the front surface, reflecting internally off the back surface, and finally refracting again as it exits the raindrop.

The light path for a primary rainbow within a raindrop includes one internal reflection. The sequence is: refraction (entry) → reflection (internal) → refraction (exit). This single internal reflection, combined with refraction and dispersion, separates the light into its constituent colours, forming the rainbow arc.

A secondary rainbow, which is fainter and appears above the primary bow with reversed colours, is formed by sunlight that undergoes two internal reflections within the raindrops. Higher-order rainbows involving three or more internal reflections are theoretically possible but are rarely observed due to significant loss of light intensity.

A non-spherical shining spoon can generally be considered as a

[amp_mcq option1=”Spherical mirror” option2=”Parabolic mirror” option3=”Plane mirror” option4=”Lens” correct=”option2″]

A shining spoon has a curved surface that acts as a mirror. While the inner part acts like a concave mirror and the outer part like a convex mirror, the curve of a spoon is generally not a perfect sphere. A common non-spherical curved mirror shape is a parabolic mirror, which has the property of focusing parallel light rays to a single point. Given that the spoon is described as ‘non-spherical’, a parabolic mirror is a suitable description for a curved mirror that is not spherical. It is definitely not a plane mirror or a lens.

A spoon’s curved, reflective surface acts as a mirror. Non-spherical curved mirrors, like parabolic mirrors, have specific shapes and optical properties.

Spherical mirrors are simpler approximations often used in basic optics. Parabolic mirrors are used in applications requiring precise focusing, such as telescopes and satellite dishes.

If the speed of light in air is $3 \times 10^8$ m/s, then the speed of light in a medium of refractive index $\frac{3}{2}$ is

[amp_mcq option1=”$2 \times 10^8$ m/s” option2=”$\frac{9}{4} \times 10^8$ m/s” option3=”$\frac{3}{2} \times 10^8$ m/s” option4=”$3 \times 10^8$ m/s” correct=”option1″]

The refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v). The formula is $n = c/v$. Given the speed of light in air (approximately equal to the speed in vacuum) $c = 3 \times 10^8$ m/s and the refractive index of the medium $n = 3/2$, we can find the speed of light in the medium ($v$) by rearranging the formula: $v = c/n$.
$v = (3 \times 10^8 \, \text{m/s}) / (3/2) = (3 \times 10^8 \, \text{m/s}) \times (2/3) = 2 \times 10^8$ m/s.

– Refractive index $n = c/v$.
– $c$ is the speed of light in vacuum (or air).
– $v$ is the speed of light in the medium.

The refractive index is a dimensionless quantity and is always greater than or equal to 1. A higher refractive index indicates a slower speed of light in the medium. The speed of light is maximum in vacuum.

In a periscope, the two plane mirrors are kept

[amp_mcq option1=”parallel to each other” option2=”perpendicular to each other” option3=”at an angle of 60° with each other” option4=”at an angle of 45° with each other” correct=”option1″]

In a simple periscope, two plane mirrors are used to change the direction of light twice. To achieve this, the mirrors are placed parallel to each other. Each mirror is typically oriented at a 45-degree angle relative to the line of sight (or the tube of the periscope) to reflect light at a 90-degree angle. The parallelism of the two mirrors ensures that the final image observed is upright relative to the object.

– A simple periscope uses two plane mirrors.
– The mirrors are placed parallel to each other.
– Each mirror is tilted at 45 degrees to the axis of the periscope.

More complex periscopes use prisms instead of mirrors to avoid issues with coatings and ensure total internal reflection, but the principle of directing light through successive reflections remains the same, often with parallel optical elements.

Which one of the following is not true about the image formed by a plane mirror?

[amp_mcq option1=”It is of the same size as the subject.” option2=”It is laterally inverted.” option3=”It is real image.” option4=”It is formed as far behind the mirror as the object is in front.” correct=”option3″]

A plane mirror forms a virtual image. A virtual image is one that cannot be projected onto a screen because the light rays do not actually converge at the location of the image; they only appear to diverge from that point. A real image, conversely, is formed where light rays actually converge and can be projected onto a screen (like the image formed by a projector or on the retina of the eye). All other statements are true properties of images formed by plane mirrors.

– Plane mirrors form virtual images.
– Virtual images cannot be projected onto a screen.
– Real images are formed by converging rays and can be projected.

Properties of image formed by a plane mirror: virtual, erect, laterally inverted, same size as object, and same distance behind the mirror as the object is in front.

Which one of the following is not a property of the X-rays?

[amp_mcq option1=”They are deflected by electric fields.” option2=”They are not deflected by magnetic fields.” option3=”They have high penetration length in matter.” option4=”Their wavelength is much smaller than that of visible light.” correct=”option1″]

X-rays are a form of electromagnetic radiation, consisting of photons. Unlike charged particles (like electrons or protons), uncharged particles like photons are generally not deflected by static electric or magnetic fields when traveling through a vacuum or air. Statement A claims they are deflected by electric fields, which is not a general property of X-rays as electromagnetic waves.

– X-rays are electromagnetic waves.
– Electromagnetic waves are not deflected by static electric or magnetic fields.
– X-rays have high penetration power and short wavelengths compared to visible light.

X-rays can be scattered by matter, and this scattering can be influenced by electromagnetic fields within the material, but the direct path of an X-ray beam is not bent by external static electric or magnetic fields in the way charged particles are.