$(a)$ Define the optical centre of a spherical lens.
$(b)$ You are given a convex lens of focal length $30 \, cm$. Where would you place an object to get a real,inverted,and highly enlarged image of the object? Draw a ray diagram showing the image formation.
$(c)$ $A$ concave lens has a focal length of $20 \, cm$. At what distance from the lens should an object be placed so that it forms an image at $15 \, cm$ away from the lens?

(N/A) The optical centre is the central point of a lens through which a ray of light passes without undergoing any deviation.
$(b)$ To obtain a real,inverted,and highly enlarged image with a convex lens,the object must be placed at the principal focus $(F_1)$. The image will be formed at infinity.
$(c)$ Given: Focal length of concave lens $f = -20 \, cm$,Image distance $v = -15 \, cm$.
Using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{-20} = \frac{1}{-15} - \frac{1}{u}$
$\frac{1}{u} = \frac{1}{-15} - \frac{1}{-20} = -\frac{1}{15} + \frac{1}{20}$
$\frac{1}{u} = \frac{-4 + 3}{60} = -\frac{1}{60}$
$u = -60 \, cm$.
Thus,the object should be placed at a distance of $60 \, cm$ in front of the lens.