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The Lensmaker's Equation is a vital formula in optics that helps us determine the focal length of a lens. It is particularly useful for lenses with different shapes and materials. The equation is written as:\[\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)\] where:- \( f \) is the focal length of the lens.- \( n \) is the refractive index of the lens material.- \( R_1 \) and \( R_2 \) are the radii of curvature of the two lens surfaces.For an equiconvex lens, like in the exercise, \( R_1 \) and \( R_2 \) have equal magnitudes but opposite signs. Calculating the focal length involves plugging in the refractive index and the radii into the equation, resulting in the precise focal length, which indicates how strong the lens is in converging or diverging light.

The lens formula is crucial for finding the image position when an object is placed near a lens. It states:\[\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\]where:- \( f \) is the focal length.- \( d_o \) is the object distance from the lens.- \( d_i \) is the image distance from the lens.To determine \( d_i \), which tells us where the image will form, we rearrange the formula. In the exercise, the given values for \( f \) and \( d_o \) were substituted to find \( d_i \). If the calculated \( d_i \) is negative, as it was here, the image is virtual, meaning it appears on the same side as the object relative to the lens.

Magnification explains how much larger or smaller the image is compared to the object. It provides insight into the dimensions and orientation of the image formed by a lens. The formula used for magnification \( m \) is:\[m = \frac{d_i}{d_o}\]Here:- A positive \( m \) indicates that the image is upright.- A negative \( m \) implies the image is inverted.- The absolute value of \( m \) shows the size ratio.In our exercise, the magnification number was \(-3\), meaning the image is three times larger than the object but inverted. This inversion for a virtual image suggests it appears flipped horizontally or vertically compared to its original orientation.

An equiconvex lens is one type of lens that bulges outward equally on both sides. This symmetrical structure is characterized by its equal radii of curvature, though one side is considered positive and the other negative because of their opposite bending directions. Key points about an equiconvex lens:

• Usually crafted from glass or similar materials and exhibits a specific refractive index.
• Used in applications requiring the convergence of light for clear and focused images.

In the exercise, the lens serves as a wall of a fish tank, bending light to create an image of objects inside the tank for an external viewer. Understanding how equiconvex lenses focus light helps explain the position and nature of the resulting image.