Sign Convention in Ray Optics

Q.

Is the relation between focal length and radius of curvature valid for lens ?

Q. A plano convex lens (f = 20 cm) is silvered at plane surface. Now f will be

Q.

A particle goes in a circle of radius 2.0 cm. A concave mirror of focal length 20 cm is placed with its principal axis passing through the centre of the circle and perpendicular to its plane. The distance between the pole of the mirror and the centre of the circle is 30 cm. Calculate the radius of the circle formed by the image.

Q. The intensity of a point source of light, S, placed at a distance d in front of a screen A, is $I_0$ at the center of the screen. Find the light intensity at the center of the screen if a completely reflecting plane mirror M is placed at a distance d behind the source, as shown in figure.

1. $\frac{27I_0}{9}$
2. $\frac{25I_0}{9}$
   
3. $\frac{17I_0}{9}$
   
   
4. $\frac{10I_0}{9}$

Q. Which types of lenses are used in telescope. With diagram.

Q. Which of the following statement is incorrect with regard to sign convention for a spherical mirror?

1. All the distances are measured from the pole.
2. The direction of incident ray is chosen to be positive.
3. The direction opposite to the incident ray is chosen to be negative.
4. The direction of the incident ray is chosen to be negative.

Q. A point source $\text{S}$ is placed at a height $h$ from the bottom of a vessel of height $H(<h)$. The vessel is polished at the base. Water is gradually filled in the vessel at a constant rate $\alpha {\text{m}}^3/\text{s}$. The distance $d$ of image of the source after reflection from the mirror, from the bottom of the vessel will be varies with time $t$ as :

1. 
2. 
3. 
4. 

Q. To measure radius of curvature of a convex mirror using a spherometer it was found that I=(4.4+-0.1)cm and h=(0.085+-0.001)cm. Calculate the maximum possible error in the radius of curvature.

Q. An object is placed at a distance of $20\text{cm}$ from a concave mirror and its real image is formed at distance of $20\text{cm}$ from the mirror. The focal length of mirror is

1. $20\text{cm}$
2. $10\text{cm}$
3. $15\text{cm}$
4. $30\text{cm}$

Q.
According to sign convention, which of the distances measured in the figure are considered to be negative?

1. a, b
2. c, b
3. a, d
4. c, d

Q. For the given object $AB$ of height $4\text{cm}$ and concave mirror of focal length $20\text{cm}$. Here, $h_o$ is the height of the object and $R$ is the radius of curvature.
Select the correct option. ( Use sign convention)

1. $h_o=+4\text{cm},R=+40\text{cm}$
2. $h_o=+4\text{cm},R=-40\text{cm}$
3. $h_o=-4\text{cm},R=+40\text{cm}$
4. $h_o=-4\text{cm},R=-40\text{cm}$

Q.

The heights of objects or images are taken as negative when measured

1. downwards, perpendicular to the principal axis

2. along the direction of incident rays

3. upwards, perpendicular to the principal axis

4. None of these

Q. An object $AB$ of height $5\text{cm}$ has been kept at a distance of $30\text{cm}$ in front of a concave mirror with radius of curvature $50\text{cm}$. Which of the following is incorrect as per sign convention?

1. Focal length of mirror is $f=+25\text{cm}$
2. Object distance is $u=-30\text{cm}$
3. Focal length of mirror is $f=-25\text{cm}$
4. Radius of curvature of mirror is $R=-50\text{cm}$

Q. What is Difference between concave and convex lens

Q. An object $AB$ of height $5\text{cm}$ has been kept at a distance of $30\text{cm}$ in front of a concave mirror with radius of curvature $50\text{cm}$. Which of the following is incorrect as per sign convention?

1. Focal length of mirror is $f=+25\text{cm}$
2. Object distance is $u=-30\text{cm}$
3. Focal length of mirror is $f=-25\text{cm}$
4. Radius of curvature of mirror is $R=-50\text{cm}$

Q. The focal length $f$ of a mirror is given by $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$, where $u$ and $v$ represent object and image distances, respectively

1. $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}$
2. $\frac{\Delta f}{f}=\frac{\Delta u}{v}+\frac{\Delta v}{u}$
3. $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}-\frac{\Delta (u+v)}{u+v}$
4. $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}+\frac{\Delta U}{u+v}+\frac{\Delta v}{u+v}$

Q. a plano convex lens is silvered at plane surface.Now f will be

Q. An object of height 10 cm is placed at a distance 100 cm before the convex mirror perpendicular below the principal axis. If the focal length of the mirror is 10 cm, on applying the Cartesian sign convention. Find the signs of object distance, focal length and height of the object.

1. $u=100cm,f=-10cm,h=-10cm$
2. $u=100cm,f=10cm,h=20cm$
3. $u=100cm,f=-10cm,h=10cm$
4. $u=-100cm,f=10cm,h=10cm$

Q. A point object $\text{O}$ is placed in front of a concave mirror of focal length $10\text{cm}$ as shown in the figure. A glass slab of refractive index $\mu =3/2$ and thickness $6\text{cm}$ is inserted between object and mirror. Find the position of final image when the distance between mirror and slab is $5\text{cm}$.

1. $15\text{cm}$ from the mirror
2. $17\text{cm}$ from the mirror
3. $12\text{cm}$ from the mirror
4. $16\text{cm}$ from the mirror

Q. With the help of appropriate ray diagram, state the sign conventions for reflection by spherical mirror.

Q. From the understanding of cartesian sign convention for reflection by spherical mirror, students took part in group discussion for FA - 1 in classroom. Who is wrong in the group discussion?
Alpesh : All the distances are measured from the pole of a mirror parallel to the principal axis.
Beena : The distances measured in the direction of incident ray are taken positive.
Chamak : The height measured upward and perpendicular to principal axis is taken negative.
Daksha : The height measured downward and perpendicular to principal axis is taken as positive.

1. Only Daksha
2. Champak and Daksha
3. Only Champak
4. Alpesh and Beena

Q. When a ray of light parallel to the principle axis is incident on a concave mirror$,$ the reflected ray

1. Passes through C
2. Passes through F
3. Passes midway between P and F
4. retraces its path

Q. For the given object $AB$ of height $4\text{cm}$ and concave mirror of focal length $20\text{cm}$. Here, $h_o$ is the height of the object and $R$ is the radius of curvature.
Select the correct option. ( Use sign convention)

1. $h_o=+4\text{cm},R=+40\text{cm}$
2. $h_o=+4\text{cm},R=-40\text{cm}$
3. $h_o=-4\text{cm},R=+40\text{cm}$
4. $h_o=-4\text{cm},R=-40\text{cm}$

Q. a) For concave mirror focal length is taken as ........
b) For convex mirror, radius of curvature is taken as ........

1. $a=positive,b=negative$
2. $a=negative,b=positive$
3. $a=positive,b=positive$
4. $a=negative,b=negative$

Q. A student while solving a problem on convex mirror makes mistake and uses - sign for focal length, and proceeds. The solution for location of image will be ______ concave mirror.

1. same as
2. either same or different from
3. having no relation with
4. different from

Q. According to Cartesian sign convention, in ray optics:

1. All distances are taken negative
2. All distances in the direction of incident ray are taken negative
3. All distances are taken positive
4. All distances in the direction of incident ray are taken positive

Q. Find the position of final image after three successive reflections taking first reflection on $m_1$

1. $-12.5cm$
2. 30 $cm$
3. 12.5 $cm$
4. $-30cm$

Q. The focal length, f of a concave mirror is:

1. Positive
2. Negative
3. Zero
4. None

Q. Give the cartesian sign convention for height of a real image?

Q. What is the nature of a mirror having a focal length, of + 10 cm?