## A doctor has prescribed a corrective lens of power

[question] Question. A doctor has prescribed a corrective lens of power $+1.5$ D. Find the focal length of the lens. Is the prescribed lens diverging or converging ? [/question] [solution] solution: Given, power, $\mathrm{P}=+1.5 \mathrm{D}$ Power, $P=\frac{1}{f}$ or $f=\frac{1}{P}=\frac{1}{+1.5}=\frac{10}{15}=+\frac{2}{3}$ or $\mathrm{f}=+0.66 \mathrm{~m}=+66 \mathrm{~cm}$ The lens is a convex (or converging) lens. [/solution]...

## Find the focal length of a lens of power

[question] Question. Find the focal length of a lens of power $-2.0 \mathrm{D}$. What type of lens is this? [/question] [solution] solution: Given, power, $P=-2.0$ D Power, $P=\frac{1}{f}$ or $f=\frac{1}{P}=\frac{1}{-2}=-0.5 \mathrm{~m}=-50 \mathrm{~cm}$ The lens is a concave (or diverging) lens. [/solution]...

## An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm.

[question] Question. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp, focussed image can be obtained ? Find the size and the nature of the image. [/question] [solution] solution: Given, object height, $\mathrm{h}_{1}=+7 \mathrm{~cm}$; object distance, $\mathrm{u}=-27 \mathrm{~cm}$; focal length, $\mathrm{f}=-18 \mathrm{~cm}$; image distance, $\mathrm{v}=? ;$ image height, $...

## An object 5.0 cm in length is placed at a distance

[question] Question. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size. [/question] [solution] solution: Given, object distance, $\mathrm{u}=-20 \mathrm{~cm}$; radius of curvature, $\mathrm{R}=+30 \mathrm{~cm}$; height of object, $h_{1}=+5 \mathrm{~cm}$; image distance, $\mathrm{v}=? ;$ magnification, $\mathrm{m}=?$ height of image, $\mathrm{h}_{2}=?$ Focal length, $\mathrm{f}=...

## The magnification produced by a plane mirror

[question] Question. The magnification produced by a plane mirror is $+1$. What does this mean ? [/question] [solution] solution: Magnification for a plane mirror is $+1$. The positive sign means the image is virtual and erect. The numerical value (magnitude) '1' means that the size of the image is exactly equal to the size of the object. [/solution]...

## An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm.

[question] Question. An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image. [/question] [solution] solution: Given, object distance, $\mathrm{u}=-10 \mathrm{~cm}$; focal length, $f=+15 \mathrm{~cm}$; image distance, $\mathrm{v}=? ;$ magnification, $\mathrm{m}=?$ Mirror formula, $\frac{1}{v}+\frac{1}{u}=\frac{1}{f} \quad$ or $\quad \frac{1}{v}+\frac{1}{(-10)}=\frac{1}{(+15)}$ or $\frac{1}{v}=\frac{1}{10}+\frac{1}{15}=\frac...

## An object 5 cm in length is held 25 cm away

[question] Question. An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and find the position, size and the nature of the image formed. [/question] [solution] solution: Given, $\mathrm{h}_{1}=+5 \mathrm{~cm} ; \mathrm{u}=-25 \mathrm{~cm}$ $\mathrm{f}=+10 \mathrm{~cm}$ By lens equation, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ or $\frac{1}{v}-\frac{1}{(-25)}=\frac{1}{+10}$ or $\frac{1}{v}+\frac{1}{25}=\frac{1}{+10}$ or $\frac{1}{v}=\frac{1}...

## One-half of a convex lens is covered with a black paper.

[question] Question. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations. [/question] [solution] solution: The convex lens will form complete image of an object, even if its one half is covered with black paper. Only the brightness of the image will reduce, in this case it will be half of the brightness of original image. It can be understood by the following two cases: (a) Le...

## Name the type of mirror used in the following situations

[question] Question. Name the type of mirror used in the following situations (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. Support your answer with reason. [/question] [solution] solution: (a) Concave mirror. Concave mirror is used in the headlights of a vehicle because it produces powerful and almost parallel beam of light when the light source is placed at its principal focus. A bulb placed at the focus of a concave mirror produces a strong, almost parall...

## Which of the following lenses would you prefer

[question] Question. Which of the following lenses would you prefer to use while reading small letters found in a dictionary? (a) A convex lens of focal length 50 cm (b) A concave lens of focal length 50 cm (c) A convex lens of focal length 5 cm (d) A concave lens of focal length 5 cm [/question] [solution] solution: Option (c) is correct. For reading small letters in a dictionary, a convex lens of small focal length is used as it is kept quite close to the page of the dictionary. [/solution]...

## No matter how far you stand from a mirror,

[question] Question. No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be (a) Plane (b) Concave (c) Convex (d) Either plane or convex [/question] [solution] solution: Option (d) is correct. A convex mirror always gives a virtual and erect image of smaller size of the object placed in front of it. Similarly, a plane mirror will always give a virtual and erect image of same size as that of the object placed in front of it. Therefore, the given mirror coul...

## A spherical mirror and a thin spherical lens

[question] Question. A spherical mirror and a thin spherical lens have each a focal length of –15 cm. The mirror and the lens are likely to be (a) Both concave (b) Both convex (c) The mirror is concave and the lens is convex (d) The mirror is convex, but the lens is concave [/question] [solution] solution: Option (a) is correct i.e., a concave mirror as well as concave lens both have negative focal length [/solution]...

## Where should an object be placed in front of

[question] Question. Where should an object be placed in front of a convex lens to get a real image of the size of the object ? (a) At the principal focus of the lens (b) At twice the focal length (c) At infinity (d) Between the optical centre of the lens and its principal focus. [/question] [solution] solution: When an object is placed at $2 \mathrm{~F}_{1}$ in front of a convex lens, its image is formed at $2 \mathrm{~F}_{2}$ on the other side of the lens. The image formed is real, inverted, a...

## The image formed by a concave mirror is observed to be virtual,

[question] Question. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object ? (a) Between the principal focus and the centre of curvature (b) At the centre of curvature (c) Beyond the centre of curvature (d) Between the pole of the mirror and its principal focus [/question] [solution] solution: Option (d) is correct. When an object is placed between the pole and principal focus of a concave mirror, the image fo...

## Which one of the following materials

[question] Question. Which one of the following materials cannot be used to make a lens ? (a) Water (b) Glass (c) Plastic (d) Clay [/question] [solution] solution: (d) Clay is not transparent, therefore it cannot be used for making lens. [/solution]...

## Find the power of a concave

[question] Question. Find the power of a concave lens of focal length 2 m. [/question] [solution] solution: Given, focal length $=-2 \mathrm{~m}$ (focal length of concave lens is negative). Power, $P=\frac{1}{f}=\frac{1}{-2.0}$ or $P=-0.5$ Dioptre [/solution]...

## A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it.

[question] Question. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also, find the power of the lens. [/question] [solution] solution: Given, $\mathrm{v}=+50 \mathrm{~cm}$ (positive sign is taken because real image in convex lens is formed on the right side). Since, the image is real and size of the image is equal to the size of object. $\therefore$ ...

## Define 1 dioptre of power of a lens.

[question] Question. Define 1 dioptre of power of a lens. [/question] [solution] solution: 1 dioptre is defined as the power of a lens of focal length 1 metre. [/solution]...

## The refractive index of diamond is

[question] Question. The refractive index of diamond is 2.42. What is the meaning of this statement ? [/question] [solution] solution: We know that, absolute refractive index (n) of a medium is given by, $n=\frac{c}{v}$ or $v=\frac{c}{n}$ i.e., $v \propto \frac{1}{n}$ Since, the refractive index of diamond is 2.42, this suggests that the speed of light in diamond will reduce by a factor 2.42 compared to its speed in air. [/solution]...

## You are given kerosene,

[question] Question. You are given kerosene, turpentine and water. Using the table given in question 3, find in which of these does the light travel fastest. [/question] [solution] solution: The light travels fastest in water as its refractive index is least $(v \propto 1 / n)$ among the three given substances. [/solution]...

## Find out, from Table given below,

[question] Question. Find out, from Table given below, the medium having highest optical density. Also find the medium with lowest optical density. [/question] [solution] solution: Among the media given in the above table, diamond has highest optical density as its refractive index is maximum among the given media. Air has least optical density as its refractive index is minimum among the given media. [/solution]...

## Light enters from air to glass having refractive index 1.50.

[question] Question. Light enters from air to glass having refractive index $1.50$. What is the speed of light in the glass ? The speed of light in vacuum is $3 \times 10^{8} \mathrm{~ms}^{-1}$. [/question] [solution] solution: We know that, absolute refractive index (n) of a medium is given by, $\mathrm{n}=\frac{\mathrm{c}}{\mathrm{v}}$ or $\mathrm{v}=\frac{\mathrm{c}}{\mathrm{n}}$ or $v_{\text {glass }}=\frac{c}{n_{\text {glass }}}=\frac{3 \times 10^{8}}{1.5}=2 \times 10^{8} \mathrm{~m} / \mat...

## A ray of light travelling in air enters obliquely into water.

[question] Question. A ray of light travelling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal ? Why ? [/question] [solution] solution: The light ray bends towards the normal. This is because it enters from rarer (air) medium to denser (water) medium. [/solution]...

## A concave mirror produces three times magnified

[question] Question. A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located? [/question] [solution] solution: Given, magnification, $m=-3$ (negative sign is taken as image is real); object distance $=-10 \mathrm{~cm}$ Now, $m=-\frac{v}{u} \quad$ or $\quad v=-m \times u$ or $\mathrm{v}=-(-3) \times(-10)=-30 \mathrm{~cm}$ [/solution]...

## Find the focal length of a convex mirror

[question] Question. Find the focal length of a convex mirror whose radius of curvature is 32 cm. [/question] [solution] solution: Given, radius of curvature, $\mathrm{R}=+32 \mathrm{~cm}$ Focal length, $f=(1 / 2) \times$ radius of curvature or $\mathrm{f}=(1 / 2) \times \mathrm{R}=(1 / 2) \times(+32)=+16 \mathrm{~cm}$ [/solution]...

## Why do we prefer a convex mirror

[question] Question. Why do we prefer a convex mirror as a rear-view mirror in vehicles ? [/question] [solution] solution: Convex mirror is preferred as a rear-view mirror because it always gives an erect, though diminished image. Also, it has a wider field of view as it is curved outwards. Thus, convex mirror enables the driver to view much larger area than would be possible with a plane mirror. [/solution]...

## Name a mirror that can give an erect

[question] Question. Name a mirror that can give an erect and enlarged image of an object. [/question] [solution] solution: Concave mirror [/solution]...

## The radius of curvature of a spherical

[question] Question. The radius of curvature of a spherical mirror is $20 \mathrm{~cm}$. What is its focal length ? [/question] [solution] solution: Given, radius of curvature, $R=20 \mathrm{~cm}$ Focal length, $\mathrm{f}=(1 / 2) \times$ radius of curvature or $\mathrm{f}=(1 / 2) \times \mathrm{R}=(1 / 2) \times 20=10 \mathrm{~cm}$ [/solution]...

## Define the principal focus of a concave mirror.

[question] Question. Define the principal focus of a concave mirror. [/question] [solution] solution: The principal focus of a concave mirror is a point on the principal axis, at which the incident rays parallel to the principal axis, after reflection, actually meet. [/solution]...