An individual is nearsighted; his near point is 11.0 cm and his far point is 51.0 cm. (a) What lens power is needed to correct his nearsightedness? 1.96 X The response you submitted has the wrong sign. diopters (b) When the lenses are in use, what is this person's near point? 11 x cm Your response differs from the correct answer by more than 10% Double check your calculations
Ray Optics
Optics is the study of light in the field of physics. It refers to the study and properties of light. Optical phenomena can be classified into three categories: ray optics, wave optics, and quantum optics. Geometrical optics, also known as ray optics, is an optics model that explains light propagation using rays. In an optical device, a ray is a direction along which light energy is transmitted from one point to another. Geometric optics assumes that waves (rays) move in straight lines before they reach a surface. When a ray collides with a surface, it can bounce back (reflect) or bend (refract), but it continues in a straight line. The laws of reflection and refraction are the fundamental laws of geometrical optics. Light is an electromagnetic wave with a wavelength that falls within the visible spectrum.
Converging Lens
Converging lens, also known as a convex lens, is thinner at the upper and lower edges and thicker at the center. The edges are curved outwards. This lens can converge a beam of parallel rays of light that is coming from outside and focus it on a point on the other side of the lens.
Plano-Convex Lens
To understand the topic well we will first break down the name of the topic, ‘Plano Convex lens’ into three separate words and look at them individually.
Lateral Magnification
In very simple terms, the same object can be viewed in enlarged versions of itself, which we call magnification. To rephrase, magnification is the ability to enlarge the image of an object without physically altering its dimensions and structure. This process is mainly done to get an even more detailed view of the object by scaling up the image. A lot of daily life examples for this can be the use of magnifying glasses, projectors, and microscopes in laboratories. This plays a vital role in the fields of research and development and to some extent even our daily lives; our daily activity of magnifying images and texts on our mobile screen for a better look is nothing other than magnification.
![### Nearsightedness Correction Example
An individual is nearsighted; his near point is **11.0 cm** and his far point is **51.0 cm**.
#### (a) What lens power is needed to correct his nearsightedness?
**Submitted Answer:** 1.96 diopters ❌
**Feedback:** The response you submitted has the wrong sign.
#### (b) When the lenses are in use, what is this person’s near point?
**Submitted Answer:** 11 cm ❌
**Feedback:** Your response differs from the correct answer by more than 10%. Double-check your calculations.
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### Explanation:
**(a) Correcting Nearsightedness**
To determine the correct lens power needed for a nearsighted person, use the formula for lens power \( P \):
\[ P = \frac{1}{f} \]
where \( f \) is the focal length. For a nearsighted person, the focal length is negative.
Given the far point \( d_{fp} \) is 51.0 cm:
\[ d_{fp} = -51 \text{ cm} \]
since the far point is behind the lens, indicating nearsightedness.
Convert the distance to meters:
\[ d_{fp} = -0.51 \text{ m} \]
Then:
\[ P = \frac{1}{-0.51} \approx -1.96 \text{ diopters} \]
The sign should be negative to indicate concave lenses, which correct nearsightedness.
**(b) Near Point with Corrective Lenses**
To find the new near point when corrective lenses are used, consider the formula:
\[ P = \frac{1}{d_{np}} + \frac{1}{d_{fp}} \]
However, since the incorrect answer is given:
1. The original calculation should be rechecked.
2. Apply proper near point formula considering lens power and new near point calculation.
For accurate results, double-check your calculations and ensure correct sign usage for distances.
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