A narrow beam of yellow light (do = 590 nm) is incident from air on a smooth surface of water at an angle of 8, = 45.0°. Determine the angle of refraction, 02, and the wavelength of the light in water. • (angle of refraction) nm (wavelength in water)
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.
![### Refraction of Yellow Light in Water
**Problem Statement:**
A narrow beam of yellow light (λ₀ = 590 nm) is incident from air on a smooth surface of water at an angle of θ₁ = 45.0°. Determine the angle of refraction, θ₂, and the wavelength of the light in water.
**Required to Determine:**
1. Angle of refraction (θ₂)
2. Wavelength in water (λ)
**Inputs:**
- Incident wavelength in air (λ₀): 590 nm
- Incident angle (θ₁): 45.0°
**Output Boxes:**
- Angle of refraction (θ₂)
- Wavelength in water (λ)
This problem involves applying Snell's Law to determine the angle at which light refracts when it passes from air into water and also requires using the relationship between wavelength and refractive index to find the wavelength of light in water.
### Explanation:
1. **Angle of Refraction (θ₂):**
To find the angle of refraction, we will use Snell's Law:
\[
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
\]
where \( n_1 \) is the refractive index of air (approximately 1), and \( n_2 \) is the refractive index of water (approximately 1.33).
2. **Wavelength in Water (λ):**
The wavelength of light in water can be found using the relationship:
\[
\lambda_2 = \frac{\lambda_1}{n_2}
\]
where \( \lambda_1 \) is the wavelength of light in air (590 nm) and \( n_2 \) is the refractive index of water (1.33).
### Visualization:
This problem does not include any graphs or diagrams, but understanding the interaction of light at the boundary between two mediums (air and water) is crucial.
Please input the values into the provided textboxes to determine the correct angle of refraction and wavelength of light in water.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faba1f8d4-a585-4f3b-81ef-bab7aed8dc88%2F798d39c7-e8ea-49e9-9ca8-fe88f061cc16%2Ftpfj4w_processed.jpeg&w=3840&q=75)
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