Sign Convention in Ray Optics

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

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 $R=-50\text{cm}$