Explain the terms: principal axis, optical centre, and principal focus of a converging lens. Also, calculate the image distance and magnification for an object placed 15 cm away from a converging lens

here are the solutions to question 7:

7. a) i) The principal axis is an imaginary straight line passing through the optical centre of the lens and perpendicular to its surfaces. ii) The optical centre is the central point of a lens through which light rays pass without undergoing any deviation. iii) The principal focus (or focal point) of a converging lens is the point on the principal axis where parallel rays of light, after passing through the lens, converge.

   b) Given:
   Object distance, $u = 15 \text{ cm}$
   Focal length of converging lens, $f = 10 \text{ cm}$

   i) Since the object is placed between $f$ ($10 \text{ cm}$) and $2f$ ($20 \text{ cm}$) for a converging lens, the image formed is real, inverted, and magnified.

   ii) To calculate the image distance ($v$), use the lens formula:

   $$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$

   Rearrange to solve for $v$:

   $$\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$$

   Substitute the given values:

   $$\frac{1}{v} = \frac{1}{10 \text{ cm}} - \frac{1}{15 \text{ cm}}$$

   Find a common denominator:

   $$\frac{1}{v} = \frac{3}{30 \text{ cm}} - \frac{2}{30 \text{ cm}}$$ $$\frac{1}{v} = \frac{1}{30 \text{ cm}}$$ $$v = 30 \text{ cm}$$

   The image distance is $\boxed{30 \text{ cm}}$.

   iii) To calculate the magnification ($M$), use the formula:

   $$M = \frac{v}{u}$$

   Substitute the values:

   $$M = \frac{30 \text{ cm}}{15 \text{ cm}}$$ $$M = 2$$

   The magnification is $\boxed{2}$.

   c) Two differences between the eye and a camera are:

   • The eye focuses by changing the focal length of its lens (accommodation), while a camera focuses by changing the distance between its lens and the film/sensor.
   • The eye uses a retina as its light-sensitive part, whereas a camera uses photographic film or a digital sensor (CCD/CMOS).

   d) Two applications of total internal reflection are:

   • Optical fibers: Used for high-speed data transmission and in medical endoscopes.
   • Periscopes and binoculars: Use prisms to reflect light, allowing for compact designs and brighter images.