Mirror Formula

Q.

An object of 5 cm is placed at a distance of 20 cm in front of a convex mirror with a radius of curvature of 30 cm. Find the position, nature, and size of the image.

Q.

An object is held at 30 cm in front of a convex mirror of a focal length 15 cm. At what distance from the convex mirror should a plane mirror be held so that images in the two mirrors coincide with each other?

Q.

At what distance from a concave mirror of focal length $10\text{cm}$ should an object $2\text{cm}$ long be placed in order to get an erect image $6\mathrm{cm}$ tall?

Q. When a concave mirror is placed facing the sun, the sun's rays converge to a point $10\text{cm}$ from the mirror. Now, an erect $2\text{cm}$ long pin is placed $15\text{cm}$ away on the principal axis of the mirror. A sharp image of this pin is obtained on a card. What would be the height of the image?

1. $4\text{cm}$
2. $3\text{cm}$
3. $6\text{cm}$
4. $2\text{cm}$

Q. A convex mirror of focal length f produces an image (1/n) th of the size of the object. The distance of the object from the mirror is

1. nf
2. f/n
3. (n + 1)f
4. (n - 1)f

Q. A convex lens of focal length 20 cm is placed coaxially with a convex mirror of radius of curvature 20 cm. The two are kept 15 cm apart from each other. A point object lies 60 cm in front of the convex lens. Draw a ray diagram to show the formation of the image by the combination. Determine the nature and position of the image formed.

Q. (a) Draw a ray diagram for the formation of image by a compound microscope.
(b) You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to constuct a compound microscope?
$\begin{array}{ccc}\text{Lenses}& \text{Power (D)}& \text{Aperture(cm)}\\ {\text{L}}_1& 3& 8\\ {\text{L}}_2& 6& 1\\ {\text{L}}_3& 10& 1\end{array}$
(c) Define resolving power of a microscope and write one factor on which it depends.

Q. An object is placed at a distance of $12\text{cm}$ from a convex mirror of radius of curvature $12\text{cm}$. Find the position of the image from mirror.

1. $+4\text{cm}$
2. $-4\text{cm}$
3. $+6\text{cm}$
4. $-6\text{cm}$

Q. A spherical convex surface of radius of curvature 2/9 m separate two media of reflective index 4/3 and 3/2 . If an object is kept in first medium at Infinity than the position of image from spherical surfaces is

Q. What will be the height of the image when an object of $2\text{mm}$ is placed at a distance $20\text{cm}$ in front of the axis of a convex mirror of radius of curvature $40\text{cm}$?

1. $20\text{mm}$
2. $10\text{mm}$
3. $6\text{mm}$
4. $1\text{mm}$

Q.

A man uses a concave mirror for shaving. He keeps his face at a distance of 25 cm from the mirror and gets an image which is 1.4 times enlarged. Find the focal length of the mirror.

Q. The radius of curvature of a convex mirror is $60\text{cm}$. When an object is placed at $B$ its image is formed at $B^{\prime }$. If size of the image is half that of the object then the distance between $B$ and $B^{\prime }$ is

1. $30\text{cm}$
2. $60\text{cm}$
3. $45\text{cm}$
4. $90\text{cm}$

Q.

A compound microscope has a magnifying power of $100$when the image is formed at infinity. The objective has a focal length of $0.5cm$and the tube length is $6.5cm$. Find the focal length of the eyepiece

Q. Define the focal plane of a Spherical Mirror.

Q. Concave mirror of radius of curvature $20\text{cm}$ has object placed $15\text{cm}$ from its pole on the principle axis. Which of the following correctly determine the position of the image, magnification and nature of image.

1. $-30\text{cm}$, $+2$, virtual
2. $-30\text{cm}$, $-2$, Real
3. $+15\text{cm}$, $-2$, Real
4. $-30\text{cm}$, $+2$, Real

Q. The distance between a real object and its image in a convex mirror of focal length $12\text{cm}$ is $32\text{cm}$. Find the size of image if the object size is $1\text{cm}$.

Q. A $2.0\text{cm}$ high object is placed at a distance of $20\text{cm}$ from a concave mirror. A real image is formed at $40\text{cm}$ from the mirror. Calculate the focal length of the mirror and the size of the image.

1. $-13.3\text{cm},4\text{cm}$
2. $+13.3\text{cm},4\text{cm}$
3. $-10.3\text{cm},2\text{cm}$
4. $+10.3\text{cm},2\text{cm}$

Q. A U - shaped wire is placed before a concave mirror having radius of curvature $20\text{cm}$ as shown in the figure. Find the total length of the image.

1. $2\text{cm}$
2. $10\text{cm}$
3. $8\text{cm}$
4. $14\text{cm}$

Q. If radii of curvature of both convex surfaces is $20\text{cm}$, then the focal length of the lens for an object placed far in air in the given arrangement is:
(consider lens to be thin)

1. $10\text{cm}$
2. $20\text{cm}$
3. $40\text{cm}$
4. $80\text{cm}$

Q. An object $\text{AB}$ is placed on the axis of concave mirror of focal length $10\text{cm}$. End $\text{A}$ of the object is at $30\text{cm}$ from mirror. Find the length of the image if length of object is $5\text{cm}$.

1. $10\text{cm}$
2. $2.5\text{cm}$
3. $1\text{cm}$
4. $0.5\text{cm}$

Q.

What are the mirror formula and magnification?

Q. A plane mirror is placed at a distance of $50\text{cm}$ from a concave mirror of focal length $16\text{cm}$. Where should a short object be placed between the mirrors and facing both the mirrors so that its virtual image in the plane mirror coincides with the real image in concave mirror?

1. $30\text{cm}$ from the concave mirror
2. $20\text{cm}$ from the plane mirror
3. $15\text{cm}$ from the concave mirror
4. $30\text{cm}$ from the plane mirror

Q. A convex mirror has a radius of curvature of $20\text{cm}$. An object is placed at such a distance from the mirror that the size of the image is exactly half that of the object. The object distance must be

1. $40\text{cm}$
2. $30\text{cm}$
3. $20\text{cm}$
4. $10\text{cm}$

Q.

Statement I : The formula connecting u, v and f for a spherical mirror is valid only for the mirrors whose sizes are very small as compared to their radii of curvature.

Statement II : Laws of reflection are strictly valid for plane surfaces, but not for larger spherical surfaces. [ IIT JEE 2007 ]

1. Statement I is correct but Statement II is incorrect
2. Statement I is incorrect but Statement II is correct
3. Both the statements are correct but Statement II doesn’t infer to Statement I
4. Both the statements are correct and statement II infers to Statement I

Q. A square of side 3 cm is placed at a distance of 25 cm from a concave mirror of focal length 10 cm. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the wire is

1. $4c{m}^2$
2. $16c{m}^2$
3. $36c{m}^2$
4. $6c{m}^2$

Q.

An object is kept at a distance of $15cm$ from a concave mirror whose radius of curvature is $30cm$. What is the position of the image?

Q. A spherical convex surface separates object and image spaces of refractive indices 1 and 4/3 respectively.If the radius of curvature of the surface is 10 cm, its power is: (1)1.5D (2)2.5 D (3)3.5 D (4)4.5

Q. 25. From a point source a light falls on a spherical glasssurface (μ 1.5 and radius of curvature- 10 cm).The distance between point source and glass surface is50 cm. The position of image is(a) 25 cmm(c) 100 cm(b) 50 cnm(d) 150 cm

Q. A convex mirror has a focal length $f$. A real object, placed at a distance $f$ in front of it from the pole, produces an image at

1. $2f$
2. $f$
3. $\infty$
4. $\frac{f}{2}$

Q. Light is incident on a thin lens as shown in figure. The radius of curvature of both the surfaces is $R$. The focal length for this system will be

1. $\frac{{\mu }_2-{\mu }_1}{R}$
2. $\frac{{\mu }_{3}R}{{\mu }_3-{\mu }_1}$

3. $\frac{{\mu }_{3}R}{{\mu }_1}$

4. $\frac{{\mu }_2}{R}{\mu }_2-{\mu }_1$