The near point of a person's eye is 60.0 cm. What is the approximate power of the correcting lens that allows the person clearly see objects placed 30.0 cm away? Neglect the eye-lens distance. O (A) -5.00 diopters O (B) -1.67 diopters O (C) +1.67 diopters O (D) +5.00 diopters Need Help? Read It

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Question:**

The near point of a person's eye is 60.0 cm. What is the approximate power of the correcting lens that allows the person to clearly see objects placed 30.0 cm away? Neglect the eye-lens distance.

**Options:**

(A) -5.00 diopters  
(B) -1.67 diopters  
(C) +1.67 diopters  
(D) +5.00 diopters  

**Need Help?**

[Read It] (button)

---

**Explanation:**

To solve this problem, we need to use the lens formula:

\[ \frac{1}{f} = \frac{1}{d_o} - \frac{1}{d_i} \]

Where:
- \( f \) is the focal length of the lens,
- \( d_o \) is the object distance,
- \( d_i \) is the image distance (which is the near point of the eye).

Since the power \( P \) of a lens in diopters is given by \( P = \frac{1}{f} \) (when \( f \) is in meters), we need to first find the focal length \( f \).

Given:
- The near point \( d_i = 60.0 \) cm \( = 0.60 \) m (since 1 cm = 0.01 m),
- Object distance \( d_o = 30.0 \) cm \( = 0.30 \) m.

Using the lens formula:
\[ \frac{1}{f} = \frac{1}{0.30} - \frac{1}{0.60} \]

\[ \frac{1}{f} = \frac{1}{0.30} - \frac{1}{0.60} \]
\[ \frac{1}{f} = \frac{2}{0.60} - \frac{1}{0.60} \]
\[ \frac{1}{f} = \frac{1}{0.60} \]
\[ f = 0.60 \text{ m} \]

Then, the power \( P \) of the lens:
\[ P = \frac{1}{f} = \frac{1}{0.60} \approx 1.67 \text{ diopters} \]

So, the correct answer is:

(C) +1.67 diopters
Transcribed Image Text:**Question:** The near point of a person's eye is 60.0 cm. What is the approximate power of the correcting lens that allows the person to clearly see objects placed 30.0 cm away? Neglect the eye-lens distance. **Options:** (A) -5.00 diopters (B) -1.67 diopters (C) +1.67 diopters (D) +5.00 diopters **Need Help?** [Read It] (button) --- **Explanation:** To solve this problem, we need to use the lens formula: \[ \frac{1}{f} = \frac{1}{d_o} - \frac{1}{d_i} \] Where: - \( f \) is the focal length of the lens, - \( d_o \) is the object distance, - \( d_i \) is the image distance (which is the near point of the eye). Since the power \( P \) of a lens in diopters is given by \( P = \frac{1}{f} \) (when \( f \) is in meters), we need to first find the focal length \( f \). Given: - The near point \( d_i = 60.0 \) cm \( = 0.60 \) m (since 1 cm = 0.01 m), - Object distance \( d_o = 30.0 \) cm \( = 0.30 \) m. Using the lens formula: \[ \frac{1}{f} = \frac{1}{0.30} - \frac{1}{0.60} \] \[ \frac{1}{f} = \frac{1}{0.30} - \frac{1}{0.60} \] \[ \frac{1}{f} = \frac{2}{0.60} - \frac{1}{0.60} \] \[ \frac{1}{f} = \frac{1}{0.60} \] \[ f = 0.60 \text{ m} \] Then, the power \( P \) of the lens: \[ P = \frac{1}{f} = \frac{1}{0.60} \approx 1.67 \text{ diopters} \] So, the correct answer is: (C) +1.67 diopters
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