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Step-by-Step Solution
Step 1: Identify the given data
• Power of cornea: $P_{\text{cornea}} = +40\,\text{D}$
• Least converging power of eye lens: $P_e = +20\,\text{D}$
Step 2: Calculate the total power of the eye (cornea + lens)
The total power $P_{\text{total}}$ is the sum of the powers of the cornea and the eye lens:
$P_{\text{total}} = P_{\text{cornea}} + P_e = 40 + 20 = 60\,\text{D}$
Step 3: Determine the focal length of the combined system
By definition, power in dioptres (D) is given by $P = \frac{1}{f}$, where $f$ is in meters.
Therefore,
$$
f = \frac{1}{P_{\text{total}}} = \frac{1}{60}\,\text{m}.
$$
Converting meters to centimeters:
$$
f = \frac{1}{60} \times 100\,\text{cm} = \frac{100}{60}\,\text{cm} = \frac{5}{3}\,\text{cm} \approx 1.67\,\text{cm}.
$$
Step 4: Use the lens formula to double-check the image distance
For the minimum converging state of the eye lens, the object is effectively at infinity ($u = -\infty$) and we want the image to be formed on the retina ($v$). Using the lens formula:
$$
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}.
$$
Since $u = -\infty$, $\frac{1}{u} = 0$, so
$$
\frac{1}{v} = \frac{1}{f} \implies v = f = \frac{5}{3}\,\text{cm}.
$$
Step 5: Conclude the distance between the retina and the cornea-lens system
The image distance $v$ is the distance between the retina and the cornea-lens system. Hence,
$$
\text{Distance between retina and cornea-lens} = \frac{5}{3}\,\text{cm} \approx 1.67\,\text{cm}.
$$
Final Answer
The distance between the retina and the cornea-eye lens is approximately $1.67\,\text{cm}$.
