6 Most SAQ’s of Ray Optics and Optical Instruments Chapter in Inter 2nd Year Physics (TS/AP)

4 Marks

SAQ-1 : Define critical angle. Explain total internal reflection using a neat diagram.

Introduction

The “critical angle” is a key concept in physics, especially in the study of light and optics. It’s important to understand when and how light changes its path, especially when it goes from one material to another, like from water to air or glass to air.

1. Defining Critical Angle: The critical angle is the angle of incidence that provides an angle of refraction of 90-degrees. When light moves from a denser medium (like water or glass) to a less dense medium (like air) and the incident angle is bigger than the critical angle, light doesn’t pass into the second medium. Instead, it turns back into the first medium.
2. Understanding Total Internal Reflection: Total Internal Reflection (TIR) happens when the angle of incidence is larger than the critical angle. This means that all the light is reflected back into the original medium. A good example of this is looking up while underwater. The light doesn’t leave the water; instead, it bounces back, which is why you see a reflection.
3. Steps of Total Internal Reflection:
   • Light travels from a denser medium to a less dense medium.
   • The angle of incidence is larger than the critical angle.
   • Instead of refracting and passing into the less dense medium, the light reflects entirely back into the denser medium.
   • This is Total Internal Reflection.

Summary

The critical angle and total internal reflection are key parts of how light behaves. These principles are fundamental in different fields, like optics, fiber-optic communications, and even natural phenomena like rainbows and mirages. Remember, the critical angle is the angle of incidence that causes refraction at 90-degrees, and total internal reflection occurs when all the light reflects back into the denser medium because the incident angle is greater than the critical angle.

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SAQ-2 : Explain the formation of a mirage.

Introduction

A “mirage” is a term used in optics, which refers to the misleading appearance of objects at a distance. It is an optical illusion that’s caused by the refraction, or bending, of light rays through layers of air that have different densities. It’s often seen in deserts or on hot roads, appearing like a puddle of water at a distance. The concept of total internal reflection plays a key role in creating a mirage.

1. Understanding Light Refraction: Before we get to mirages, we need to understand refraction. Refraction is the change in direction of light when it passes from one medium to another, like from air to water or air to glass. When light goes from a denser medium to a less dense medium, it bends away from the normal line. The “normal” is an imaginary straight line that’s perpendicular to the surface at the point of incidence, where the light hits.
2. Formation of a Mirage: Mirages occur due to the refraction and total internal reflection of light by different layers of air. Here are the steps:
   • On a hot day, the air just above the ground becomes hotter (and hence less dense) than the air above it.
   • Light from the sky, when it reaches this hot air near the surface, moves from a denser medium to a less dense medium
   • Due to refraction, the light bends away from the normal, making an angle larger than the critical angle with the normal at the interface of the hot and cool air layers
   • This leads to the total internal reflection of light.
   • The reflected light when reaches our eyes, our eyes trace it back as a straight line (since we typically perceive light to travel in a straight path).
   • This gives the illusion of the sky (or a body of water) on the ground, which is the mirage we see.
3. Importance of Mirage: Understanding mirages helps us in studying how light behaves when it moves through mediums of different densities. This is particularly important in areas such as meteorology and environmental studies, as well as in understanding optical illusions and certain natural phenomena.

Summary

So, in simple terms, a mirage is a natural optical illusion that happens when light refracts and reflects due to changes in air density. This event, often seen on hot days, makes it appear like there is water or the sky on the ground. It’s a fascinating example of the principles of refraction and total internal reflection in action. Understanding these concepts not only explains this natural phenomenon but also helps in grasping more complex principles in physics and optics.

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SAQ-3 : Explain the formation of a rainbow.

Introduction

A rainbow is a beautiful and natural phenomenon that occurs in the sky, particularly after it rains. It’s a multi-colored arc that has seven colors, which are violet, indigo, blue, green, yellow, orange, and red. The formation of a rainbow involves three main steps: dispersion, refraction, and internal reflection of sunlight inside raindrops.

Understanding Light

Before explaining a rainbow, let’s understand light. Sunlight, also called white light, is actually a mix of different colors. Each color has a different wavelength, and when they all come together, we see it as white light.

How Rainbow Forms

1. Dispersion: When sunlight enters a raindrop, it breaks apart into different colors. This happens because each color bends, or refracts, by a slightly different amount. This spreading of white light into its full spectrum of colors is called dispersion.
2. Internal Reflection: The dispersed light inside the raindrop hits the inside surface of the raindrop and reflects off it. This is the internal reflection. Some light does escape from the raindrop, but a significant amount of it reflects back inside.
3. Refraction Again: This internally reflected light then hits the surface of the raindrop again and refracts out of the raindrop.
4. Order of Colors: Each color emerges at a slightly different angle. The red light comes out at the steepest angle, and the violet light comes out at the least steep angle. This is why the red color is at the top of the rainbow, and violet is at the bottom.
5. Observer’s Position: We see a rainbow when our back is to the sun, and we’re looking at an approximately 40-42 degree angle away from the direction opposite the sun.

Summary

So, a rainbow is a lovely natural event that happens when sunlight gets spread out into different colors, and then gets bounced inside raindrops and comes out to our eyes. The sunlight goes through dispersion, then reflects inside the raindrop, and refracts out again. When we see this light, we see it as a circular arc of colors with red on the outer part and violet on the inner part.

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SAQ-4 : With a neat labelled diagram explain the formation of image in a simple microscope.

Introduction

A simple microscope, also known as a magnifying glass, uses a convex lens with a short focal length to create a magnified image of small objects. Let’s understand the working of a simple microscope with a ray diagram and derive the magnification formula.

Ray Diagram and Working of a Simple Microscope

1. Picture a convex lens with its principal focus (F) and optical center (O). The object AB is placed between F and O.
2. A light ray from point A of the object that is parallel to the principal axis is refracted through the focus (F’) on the other side of the lens.
3. A second ray of light from point A passes through the optical center O without changing its path.
4. These refracted rays are diverging, so they seem to come from a point A’ behind the lens if we extend them backward.
5. Drawing a line perpendicular from A’ to the principal axis, we get a virtual, erect, and magnified image A’B’ of the object AB.

Magnification Formula

Magnification (m) is the ratio of the height of the image to the height of the object, which is also equal to the ratio of the image distance (v) to the object distance (u). So, $$m = \frac{v}{u}$$

In a simple microscope, the lens is adjusted so the image is formed at the near point, which is typically a distance (D) of 25cm from the eye.

1. Using the lens formula, 1/f = 1/v − 1/u, we can rearrange to find 1/u = 1/v − 1/f.
2. Substituting this in the magnification formula, we get m = v × (1/v−1/f). According to the sign convention, v = −D. Substituting this value, we get m = 1 + D/f.

Summary

So, a simple microscope uses a convex lens to make small objects appear bigger. Light rays from the object refract at the lens to form a virtual, upright, and enlarged image. The magnification can be calculated using the formula m = 1 + D/f. Understanding this process and remembering the magnification formula will help students perform better in exams. A simple microscope is a handy tool for basic purposes like reading fine print or examining small details.

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SAQ-5 : Define focal length of a concave mirror. Prove that the radius of curvature of a concave mirror is double its focal length.

Introduction

A concave mirror is a special type of mirror that curves inwards. These mirrors have a special property that if light rays parallel to the main line (principal axis) hit the mirror, they bounce off and meet at one point. This point is known as the principal focus.

1. Understanding Focal Length: The focal length is the distance from the middle of the concave mirror (the pole) to the principal focus. The way we can find the focal length is by getting a real image of an object that is far away.
2. Understanding Radius of Curvature: Imagine you have a concave mirror. Draw a line (ray) AB that runs parallel to the principal axis PC, hitting the mirror at point B. This ray then bounces off the mirror and goes through the focus, F. P is the middle of the mirror (pole), and C is the centre of the whole circle the mirror could be part of (centre of curvature). The distance PF is the focal length, f. The distance PC is the radius of the circle, R.
3. Proving the Relationship:
   • Draw a line BC that stands up straight (normal) to the mirror where the ray hits it at B. The angle ABC is equal to the angle CBF because light reflects at the same angle it hits (Law of reflection, $$\angle i = \angle r$$
   • The angle ABC is also equal to the angle BCF because they are on opposite sides of a straight line (alternate angles).
   • So, this means that $$\angle BCF = \angle CBF$$ Because these two angles are the same, triangle FBC is an isosceles triangle, where the sides opposite equal angles are the same length.
   • So, this means that BF=FC. If we imagine the mirror is very small (small aperture), the point B is very close to the point P, so BF=PF.
   • Therefore, $$PF = FC = \frac{1}{2}PC$$ or $$f = \frac{1}{2}R$$

Summary

The focal length of a concave mirror is the distance from the middle of the mirror to the focus point. The radius of curvature is the distance from the middle of the mirror to the centre of the whole circle the mirror could be part of. Using angles and triangles, we proved that the radius is twice as long as the focal length (R = 2f). This understanding is important for things like correcting short-sightedness with concave lenses, which are similar to concave mirrors but bend light instead of reflecting it. Remember, a concave mirror or a lens will only make a virtual image if the object is more than one focal length away. The image will be upright and smaller.

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SAQ-6 : Why does the setting sun appear red?

Introduction

Sunsets and sunrises are beautiful natural events that we often admire. One striking feature of these events is the change in the color of the sky and the Sun, where they often appear to be red or orange. This color change happens because of a process called scattering.

1. Understanding Light: Light, that we see every day, is composed of different colors. Each color has a different wavelength. Blue and violet light have shorter wavelengths, while red and orange light have longer wavelengths. When light travels in the atmosphere, it interacts with molecules and particles in the air. This interaction causes the light to scatter, or spread out, in different directions.
2. The Role of Scattering: The color of the sky we see depends on how much of each color of light is scattered. Shorter wavelengths (like blue and violet) are scattered more than longer wavelengths (like red and orange). This is why the sky appears blue to us during the daytime. The blue light is being scattered in all directions and thus, it is the color that we see.
3. Why Sun Appears Red during Sunset and Sunrise:
   • During sunset and sunrise, the Sun is closer to the horizon. Because of this, the sunlight has to travel a longer distance through the Earth’s atmosphere.
   • As the sunlight travels this long path, most of the short-wavelength light (blue and violet) gets scattered in different directions and moves away from your line of sight.
   • The long-wavelength light (red, orange, and yellow), however, gets scattered less and continues to move along your line of sight. Therefore, when you look at the Sun during sunrise or sunset, you see more of the longer-wavelength light, making the Sun appear red or orange.

Summary

Sunsets and sunrises are red because of a process called scattering. Light is made up of different colors, and each color scatters, or spreads out, differently when it interacts with particles in the air. Shorter wavelengths scatter more, so we normally see a blue sky. But during a sunset or sunrise, the Sun’s light has to pass through more of the Earth’s atmosphere, and the shorter wavelengths scatter out of sight. This leaves the longer wavelengths, like red and orange, for us to see, making the Sun appear red.