Practice Questions

Justify why the power of a convex lens is considered positive, while that of a concave lens is negative, based on their converging and diverging nature.

Apply the concept of refractive index to calculate the speed of light in diamond, given that the absolute refractive index of diamond is $2.42$ and the speed of light in vacuum is $3 \times 10^8 \text{ m/s}$.

Calculate the power of a concave lens that has a focal length of $50$ cm.

Define the power of a lens and name its SI unit.

Recall the focal length of a spherical mirror whose radius of curvature is $40$ cm.

An optician prescribes a corrective lens with a power of $+2.5$ D. Calculate the focal length of this lens.

List three properties of the image formed by a plane mirror.

Recall the two laws of reflection of light.

A spherical mirror has a focal length of $-25$ cm. Analyze the sign of the focal length to identify the type of mirror.

Name the type of mirror used as a rear-view mirror in vehicles.

An optician has two thin lenses, one with power $P_1 = +4.0 \text{ D}$ and another with power $P_2 = -1.5 \text{ D}$. Propose using these lenses in contact to form a single equivalent lens. Justify the nature of the combination by calculating its net power and focal length. Evaluate its suitability for a person who needs a converging corrective lens.

Evaluate the statement: 'The magnification of a spherical mirror is given by $m = -v/u$. A negative magnification always implies that the image is smaller than the object.' Is this statement entirely correct? Justify your answer.

A student claims that a convex mirror can be used as a shaving mirror. Critique this statement. Justify your evaluation based on the properties of the image formed by a convex mirror.

A student observes that a ray of light passing through the center of curvature of a concave mirror retraces its path after reflection. Justify this observation using the laws of reflection.

Create a ray diagram for a concave mirror where the object is placed at the center of curvature, C. Using this diagram, prove that the image formed is real, inverted, and of the same size as the object.

A textbook states, 'When light enters from a rarer medium to a denser medium, it always bends towards the normal.' Critique the universality of this statement.

A driver prefers a convex mirror as a rear-view mirror because it provides a wider field of view. However, a known disadvantage is that it makes vehicles appear farther away than they actually are. Evaluate this trade-off. Justify why, despite this disadvantage, it is still the superior choice over a plane mirror for this purpose.

Explain the relationship between the radius of curvature and the focal length of a spherical mirror. Recall the formula that connects them.

Explain why a convex lens is called a converging lens and a concave lens is called a diverging lens.

A lens has a power of $-2.5$ D. Recall its focal length and identify the type of lens.

A $4$ cm tall object is placed perpendicular to the principal axis of a convex lens of focal length $20$ cm. The distance of the object from the lens is $30$ cm. Calculate the position, size, and nature of the image. Also, calculate the magnification.

Examine why a ray of light passing through the optical center of a thin lens proceeds without any deviation. Demonstrate with a simple diagram.

Analyze the characteristics of an image formed by a concave mirror that is virtual, erect, and larger than the object. Based on this, determine the position of the object relative to the mirror's pole (P), principal focus (F), and center of curvature (C).

Compare and contrast the characteristics of an image formed by a convex mirror and a concave lens when an object is placed at any finite distance in front of them.

An object is placed at the center of curvature (C) of a concave mirror. Demonstrate the path of two rays to locate the image and calculate the magnification produced.

Compare the field of view of a plane mirror, a concave mirror, and a convex mirror, all of the same aperture. Based on your analysis, explain why a convex mirror is preferred as a rear-view mirror in vehicles.

Two thin lenses are placed in contact. One is a convex lens of power $+4.0$ D and the other is a concave lens of power $-1.5$ D. Apply the formula for combination of lenses to calculate the power and focal length of the combination. Analyze if the combination will behave as a converging or diverging lens.

Recall the mirror formula and define each term in it.

Define the absolute refractive index of a medium in terms of the speed of light.

Describe the New Cartesian Sign Convention used for spherical mirrors. List the five main rules.

A spherical mirror has a focal length of $+15$ cm. Identify the type of mirror and explain your reasoning.

An object is placed $10$ cm in front of a convex mirror with a radius of curvature of $30$ cm. Calculate the position and magnification of the image.

Design an experiment to determine the approximate focal length of an unknown convex lens and a concave mirror using a distant object. Justify your choice of method and list the precautions required for accuracy and safety.

Explain the phenomenon of refraction of light and state the two laws of refraction. Include the mathematical expression for Snell's law.

A ray of light traveling in air is incident on a glass slab at an angle of $45^\circ$. If the refractive index of the glass is $1.50$, apply Snell's law to calculate the angle of refraction inside the glass slab. (Given $\sin(45^\circ) \approx 0.707$)

An optical instrument produces an image with a magnification of $m = +0.5$. Analyze this information to determine the type of mirror or lens that could be used and describe the nature of the image.

Design a procedure to verify the mirror formula, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$, for a given concave mirror, a candle, a screen, and a meter scale.

Propose a reason why a diamond ($n \approx 2.42$) bends light more significantly than glass ($n \approx 1.5$). Justify your proposal using Snell's Law.

Design a simple optical instrument, like a basic projector, using a single convex lens to project a magnified, real image of a slide onto a screen. (a) Specify where the slide (object) should be placed relative to the lens's principal focus (F) and twice the focal length (2F). (b) Justify your design choice using ray diagram principles. (c) Evaluate how changing the distance between the lens and the slide would affect the image.

Create a problem scenario involving a convex lens where the final image is real, inverted, and three times the size of the object. Formulate the values for the object distance ($u$) and image distance ($v$) if the focal length of the lens is $f = +20 \text{ cm}$.

Formulate a general rule to distinguish between a plane mirror, a concave mirror, and a convex mirror without touching them, by observing your image as you move closer to and farther from each mirror.

Summarize the characteristics (nature, position, and relative size) of the image formed by a concave mirror when the object is placed at the following positions: (a) at infinity, (b) at the center of curvature (C), and (c) between the pole (P) and the principal focus (F).

An object is placed in front of a convex lens. Formulate the conditions on the object distance, $u$, in terms of the focal length, $f$, for which the lens produces: (a) a real, inverted, and magnified image, and (b) a virtual, erect, and magnified image. Justify your conditions.

An object of height $5$ cm is placed $20$ cm in front of a concave mirror with a focal length of $15$ cm. Solve for the position, size, and nature of the image formed. Demonstrate this by drawing a ray diagram.