Hanhyun and Gwangwoo are experimenting with lenses. They take a double convex lens with radii R1-9.00 cm and R2 = 11.0 cm. If the lens has a focal length of 5 cm in air, what is its index of refraction in cm? What is its focal length in cm in water which has an index of refraction of 1.33?
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.
![**Experimenting with Lenses: A Student Activity**
**Objective:**
Hanhyun and Gwangwoo are experimenting with lenses to understand the focal lengths and indices of refraction in different mediums.
**Background:**
They have selected a double convex lens with the following specifications:
- Radius of curvature, R1 = 9.00 cm
- Radius of curvature, R2 = 11.0 cm
- Focal length in air, f_air = 5 cm
**Questions:**
1. What is the index of refraction of the lens in air?
2. What is its focal length in water, which has an index of refraction of 1.33?
**Formulae:**
1. Lens Maker's Equation:
\[
\frac{1}{f} = (n-1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)
\]
2. Adjusting focal length when placed in a different medium:
\[
\frac{1}{f_{medium}} = \left(\frac{n_{lens}}{n_{medium}} - 1 \right)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)
\]
**Instructions:**
1. Substitute the given values into the Lens Maker's Equation to find the index of refraction in air.
2. Use the index of refraction found in part 1, along with the given index of refraction of water, to find the new focal length of the lens in water.
**Diagram:**
Unfortunately, no graphical representation is provided in the original text. However, a schematic representation of a double convex lens with radii R1 and R2 and focal points can be helpful for understanding.
Such calculations and practical activities will deepen understanding of light behavior through different media and enhance comprehension of core optical principles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb865a02-7408-4eb8-b9f3-2c56928a70f5%2F983aa861-54fe-46e3-8649-50dc054898a8%2Foqmql2l_processed.png&w=3840&q=75)
Step by step
Solved in 2 steps with 2 images
