Mirror Formula

Q.

If a mans face is $25cm$ in front of a concave shaving mirror producing an erect image $1.5$ times the size of the face, the focal length of the mirror would be

1. $75cm$

2. $25cm$

3. $15cm$

4. $60cm$

Q.

An arrow $2.5cm$ high is placed at a distance of $25cm$ from a diverging mirror of a focal length of $20cm$. Find the nature, position, and size of the image formed.

Q.

An object is placed in front of a convex mirror at 60 m from the mirror. Its radius of curvature is 40 m. The object starts moving towards the mirror at $20\frac{m}{s}$. Find the average speed of the image after a time interval of 2 sec?

1. 2. 5

2. 20

3. 10

4. 5

Q. Which of the following relation is true for focal length (f) and the radius of curvature (R)?

1. R = 3 f
2. R = 2 f
3. R = 4 f
4. R = f

Q.

An object is placed at 20 m in front of a concave mirror. If its radius of curvature is 40 m, then the image distance is equal to ___ m.

Q. An object of size 4 cm is placed at a distance of 30 cm in front of a concave mirror of radius of curvature 20 cm. Find the position ($v$) and size ($h_i$) of the image.

1. 
   $v$ = 5 cm, $h_i$ = 4 cm
   
2. 
   $v$ = 40 cm, $h_i$ = - 1.5 cm
3. $v$ = -15 cm, $h_i$ = -2 cm
4. 
   $v$ = 15 cm, $h_i$ = -4 cm
   

Q.

Is it possible to have a real image of a real object formed

1. By a plane mirror?
2. By a concave mirror?
3. By a convex mirror?

Q. An object of size 50 cm, placed in front of a spherical mirror at 20 cm, forms an image of size 25 cm above the principal axis. Find out the focal length with sign convention and the type of spherical mirror used?

1. – 25 $cm$, concave mirror

2. – 20 $cm$, concave mirror

3. + 25$cm$, convex mirror

4. + 20 $cm$, convex mirror

Q.

A point object forms a real, enlarged image, in front of a concave mirror of curvature radius 40 cm. If the distance between the object and the image be 30 cm, what will be the object distance?

1. 40 cm

2. 60 cm

3. 10 cm

4. 30 cm

Q.

A ray starting from the focus of a concave mirror becomes parallel to the principal axis after reflection.

1. True

2. False

Q. Ratio of height of the image to the height of the object is called the ___ of the spherical mirror.

1. radius of curvature
2. focus
3. magnification
4. focal length

Q. An object is placed at a distance of 20 cm from a concave mirror of radius of curvature 0.6 m. Which of the following statement is incorrect?

1. The image is formed at a distance of 60 cm from the mirror.
2. The image formed is real.
3. Magnitude of image distance = 3times of magnitude of object distance.
4. The image formed is upside down.

Q.

Mark out the correct statement(s) for the image formed by a plane mirror.

1. It can be real.

2. It can be inverted.

3. It must be virtual and erect.

4. It must be virtual and erect for the real and extended objects.

Q. An object OA is placed in front of the concave mirror as given in the image. The point F is the focal length of the mirror and P is the pole. Determine the distance of the image from the pole of the concave mirror.

1. $66.66cm$
2. $66.66cm$
3. $33.33cm$
4. $33.33cm$

Q. An object is placed at 30 m in front of a concave mirror. If its radius of curvature is 20 m, then what will be its image distance?

1. -15 m
2. +7 m
3. -7 m
4. +15 m

Q. An object is placed at $20m$ in front of a concave mirror. If its radius of curvature is $40m$, then the image distance is equal to:

1. $60m$
2. Infinity
3. $40m$
4. $20m$

Q.

When an object is moved a distance $x$ away from a plane mirror, the distance between the object and its image increases by $2x$. Give reason.

Q. A concave mirror, of aperture $4cm$, has a point object placed on its principal axis at a distance of $10cm$ from the mirror. The image, formed by the mirror, is not likely to be a sharp image. State the likely reason for the same.

Q.

If an object moves 5 $\frac{m}{sec}$ towards the mirror. And the mirror also moves 5 $\frac{m}{sec}$ towards the object. Then find out velocity by which image will move?

1. 5 m/s, towards the mirror

2. 10 m/s, towards the mirror

3. 25 m/s, towards the mirror

4. 15 m/s, towards the mirror

Q. A spherical convex surface separates object and image spaces of refractive index 1and 4/3 . If radius of curvature of surface is 10cm, its power is 1.5D 2.5D 3.5D 3/7D

Q.

An object is placed at a distance of $25\mathrm{cm}$ from a spherical mirror and its image is formed behind the mirror at a distance of $5\mathrm{cm}$. Find focal length. Is it a concave or convex mirror?

Q. If for a spherical mirror object distance, $u=(50.1\pm 0.5)cm$ and image distance $v=(20.1\pm 0.2)cm$, then focal length of the spherical mirror will be

1. $(14.3\pm 0.1)cm$
2. $(14.3\pm 0.5)cm$
3. $(30.1\pm \pm 0.1)cm$
4. $25.3\pm 0.5)cm$

Q. An object is placed at 60 m in front of a concave mirror. If its radius of curvature is 40 m, then the image distance is equal to ___ m.

Q. Which of the following is not the characteristics of an image formed by a convex mirror?

1. Image is virtual.
2. Image lies between pole and focus.
3. Image is real.
4. Image is diminished.

Q. An object is placed at \(60~ m\) in front of a concave mirror. If its radius of curvature is \(40~ m\), then find the image distance.[3 marks]

Q. A boy of height $1m$ stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image is: (Assume paraxial ray approximation holds)

1. $0.25m$
2. $0.33m$
3. $0.67m$
4. $0.5m$

Q.

A point object is placed at a distance of 30 cm from a convex mirror of focal length 30 cm. The image will form at

1. Infinity

2. 15 cm behind the mirror

3. 15 cm infront of the mirror

4. Pole

Q. For concave mirror, paraxial rays are focused at distance $\frac{R}{2}$ from pole and marginal rays are focused at distance $x$ from pole, then

1. $x=-f$
2. $x=\frac{R}{2}$
3. $x>\frac{R}{2}$
4. $x<\frac{R}{2}$

Q. A concave mirror has a radius of curvature of 24 cm. How far is the object from the mirror if the image formed is 3 times the size of object?

Q. If $u$ represents object distance from pole of spherical mirror and $v$ represents image distance pole of mirror and $f$ is the focal length or the mirror, then a straight line $u=v$ will cut $u$ versus $v$ graph at

1. $(f,f)$
2. $(2f,2f)$
3. $(0,0)$
4. $(f,2f)$