Where is the image formed when an object is placed between the principal focus $(F)$ and the center of curvature $(C)$ of a concave mirror?

The refractive index of water with respect to air is $\frac{4}{3}$ and the refractive index of glass with respect to air is $\frac{3}{2}$. What is the refractive index of glass with respect to water?

$(a)$ State the relation between object distance,image distance and the focal length of a spherical mirror.
$(b)$ Draw a ray diagram to show the image formed by a concave mirror when an object is placed between the pole and focus of the mirror.
$(c)$ $A$ concave mirror of focal length $15\, cm$ forms an image of an object kept at a distance of $10\, cm$ from the mirror. Find the position,nature and size of the image formed by it.

$(a)$ Two lenses have powers of $(i) +2 \text{ D}$ and $(ii) -4 \text{ D}$. What is the nature and focal length of each lens?
$(b)$ An object is kept at a distance of $100 \text{ cm}$ from a lens of power $-4 \text{ D}$. Calculate the image distance.

Write the relationship between object distance $(u)$,image distance $(v)$,and focal length $(f)$ for a spherical mirror.

An object of height $5 \, cm$ is placed perpendicular to the principal axis of a concave lens of focal length $10 \, cm$. If the distance of the object from the optical centre of the lens is $20 \, cm$,determine the position,nature,and size of the image formed using the lens formula.