Optics- Reflection of Light and Formation of Images

Topic: Extended Objects

  • When light falls on an object, it undergoes reflection as per the laws of reflection.
  • The incident ray, reflected ray, and the normal to the surface at the point of incidence, all lie in the same plane.
  • The angle of incidence is equal to the angle of reflection.
  • An image of the object is formed due to the reflection of light rays from the surface of the object.
  • For extended objects, the image formed is the combination of images from different points on the object.

Properties of Image Formed by Plane Mirror

  • Image formed by a plane mirror is virtual, erect, and of the same size as the object.
  • The distance of the image from the mirror is equal to the distance of the object from the mirror.
  • The image formed is laterally inverted, i.e., right appears as left and vice-versa.

Image Formation by Spherical Mirrors

  • Spherical mirrors are made by part of a sphere.
  • There are two types of spherical mirrors: concave and convex.
  • The concave mirror is converging, whereas the convex mirror is diverging.
  • Object distance (u), image distance (v), and focal length (f) are the three parameters used to describe the image formed by spherical mirrors.

Image Formation by Concave Mirror

  • When the object is placed beyond the center of curvature of the concave mirror, a real and inverted image is formed between the focus and the center of curvature.
  • When the object is placed at the center of curvature, the image formed is real and inverted, but of the same size as the object.
  • When the object is placed between the center of curvature and the focus, the image formed is real, inverted, and magnified.

Image Formation by Convex Mirror

  • Convex mirror always forms a virtual, erect, and diminished image.
  • The image formed is located between the focus and the pole of the mirror.
  • The image formed is small, and its size decreases as the object distance increases.

Magnification by Spherical Mirrors

  • Magnification (m) is the ratio of the height of the image (h’) to the height of the object (h).
  • For spherical mirrors, magnification can be calculated using the formula: m = -v/u = h’/h.
  • Magnification is positive for an erect image and negative for an inverted image.

Mirror Formula

  • The mirror formula states that 1/v + 1/u = 1/f, where v is the image distance, u is the object distance, and f is the focal length.
  • The mirror formula relates the distance of the object, image, and focal length of a spherical mirror.
  • The sign convention is used to determine the sign of different parameters in the mirror formula.

Laws of Refraction

  • When a light ray traveling in one medium enters another medium, it undergoes a change in direction. This phenomenon is known as refraction of light.
  • The direction of light bends when it passes from one medium to another due to the change in its speed.
  • The laws of refraction include Snell’s law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media.

Refractive Index

  • Refractive index (n) is a measure of how much light is refracted when entering a new medium.
  • It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v), i.e., n = c/v.
  • The refractive index depends on the material of the medium and the wavelength of light.
  • It is a dimensionless quantity and is always greater than or equal to one. I apologize for the error in my previous response. Here are the next set of slides in the requested format:
Optics- Reflection of Light and Formation of Images - Extended Objects

Slide 11:

  • The concept of Extended Objects in optics refers to objects that have dimensions and are not simply points.
  • When light falls on an extended object, each point on the object acts as a source of light.
  • The light rays from different points on the object undergo reflection and form an image.

Slide 12:

  • The image formed by extended objects is a combination of images formed by different points on the object.
  • Each point on the object forms its own image, and all these images combine to give the final image of the object.
  • The properties of the individual images, such as size, orientation, and position, determine the overall image formed by the extended object.

Slide 13:

  • The position and size of the final image formed by an extended object depend on the shape and orientation of the object.
  • The distance of each point on the object from the reflecting surface also affects the overall image formed.
  • Understanding the formation of images by extended objects is essential for analyzing real-world scenarios and optical systems.

Slide 14:

  • To determine the position and size of the image formed by an extended object, we consider the reflection of light rays from different points on the object.
  • The laws of reflection still apply, where the incident ray, reflected ray, and the normal to the surface at the point of incidence lie in the same plane.
  • The angle of incidence is equal to the angle of reflection for each light ray from different points on the extended object.

Slide 15:

  • For example, consider a straight object, such as a ruler, placed perpendicular to a plane mirror.
  • The top point of the ruler will form an image as if it is reflected from a point above the ruler’s base.
  • The bottom point of the ruler will form an image as if it is reflected from a point below the ruler’s base.
  • All the points in between the top and bottom will also have their respective images formed accordingly.

Slide 16:

  • The final image formed by the extended object is obtained by connecting the corresponding points on each individual image.
  • This connects the top point of the ruler image to the top point of the object, and the bottom point of the ruler image to the bottom point of the object.
  • The connected points form a virtual image that appears to be behind the mirror.
  • The size and the orientation of the final image depend on the relative positions of the points on the object and the mirror.

Slide 17:

  • The final image formed by an extended object in a plane mirror is always virtual and erect.
  • The image appears to be located behind the mirror, and its size is the same as that of the object.
  • The relative positions of the object and the mirror determine whether the image is laterally inverted or not.

Slide 18:

  • For example, if an extended object is placed perpendicular to a plane mirror, the final image appears to be located exactly behind the mirror, and it is an exact replica of the object.
  • This type of lateral inversion is commonly observed when we see our own reflection in a mirror.

Slide 19:

  • On the other hand, if an extended object is placed at an angle to a plane mirror, the final image will still be located behind the mirror, but it will be laterally inverted.
  • This means that the left side of the object will appear on the right side of the image, and vice versa.
  • The extent of lateral inversion depends on the angle between the object and the mirror surface.

Slide 20:

  • Understanding the formation of images by extended objects in plane mirrors helps us analyze the behavior of light rays and predict how objects will appear when reflected.
  • It is essential to consider the position, size, orientation, and lateral inversion of the image to accurately describe the optical properties of extended objects in reflection.

Slide 21:

  • The concept of Extended Objects in optics refers to objects that have dimensions and are not simply points.
  • When light falls on an extended object, each point on the object acts as a source of light.
  • The light rays from different points on the object undergo reflection and form an image.
  • The image formed by extended objects is a combination of images formed by different points on the object.
  • Each point on the object forms its own image, and all these images combine to give the final image of the object.

Slide 22:

  • The properties of the individual images, such as size, orientation, and position, determine the overall image formed by the extended object.
  • The position and size of the final image formed by an extended object depend on the shape and orientation of the object.
  • The distance of each point on the object from the reflecting surface also affects the overall image formed.
  • Understanding the formation of images by extended objects is essential for analyzing real-world scenarios and optical systems.
  • To determine the position and size of the image formed by an extended object, we consider the reflection of light rays from different points on the object.

Slide 23:

  • The laws of reflection still apply, where the incident ray, reflected ray, and the normal to the surface at the point of incidence lie in the same plane.
  • The angle of incidence is equal to the angle of reflection for each light ray from different points on the extended object.
  • For example, consider a straight object, such as a ruler, placed perpendicular to a plane mirror.
  • The top point of the ruler will form an image as if it is reflected from a point above the ruler’s base.
  • The bottom point of the ruler will form an image as if it is reflected from a point below the ruler’s base.

Slide 24:

  • All the points in between the top and bottom will also have their respective images formed accordingly.
  • The final image formed by the extended object is obtained by connecting the corresponding points on each individual image.
  • This connects the top point of the ruler image to the top point of the object, and the bottom point of the ruler image to the bottom point of the object.
  • The connected points form a virtual image that appears to be behind the mirror.
  • The size and the orientation of the final image depend on the relative positions of the points on the object and the mirror.

Slide 25:

  • The final image formed by an extended object in a plane mirror is always virtual and erect.
  • The image appears to be located behind the mirror, and its size is the same as that of the object.
  • The relative positions of the object and the mirror determine whether the image is laterally inverted or not.
  • For example, if an extended object is placed perpendicular to a plane mirror, the final image appears to be located exactly behind the mirror, and it is an exact replica of the object.
  • This type of lateral inversion is commonly observed when we see our own reflection in a mirror.

Slide 26:

  • On the other hand, if an extended object is placed at an angle to a plane mirror, the final image will still be located behind the mirror, but it will be laterally inverted.
  • This means that the left side of the object will appear on the right side of the image, and vice versa.
  • The extent of lateral inversion depends on the angle between the object and the mirror surface.
  • Understanding the formation of images by extended objects in plane mirrors helps us analyze the behavior of light rays and predict how objects will appear when reflected.
  • It is essential to consider the position, size, orientation, and lateral inversion of the image to accurately describe the optical properties of extended objects in reflection.

Slide 27:

  • In addition to plane mirrors, the formation of images by extended objects can also be studied in spherical mirrors.
  • Spherical mirrors are curved mirrors that are part of a sphere.
  • They are classified into two types: concave and convex mirrors.
  • Concave mirrors are converging mirrors, while convex mirrors are diverging mirrors.
  • The shape and curvature of the mirror determine the characteristics of the images formed by spherical mirrors.

Slide 28:

  • When an extended object is placed in front of a concave mirror, the image formed depends on the position of the object with respect to the mirror.
  • If the object is placed beyond the center of curvature of the concave mirror, a real and inverted image is formed between the focus and the center of curvature.
  • If the object is placed at the center of curvature, the image formed is real and inverted, but of the same size as the object.
  • If the object is placed between the center of curvature and the focus, the image formed is real, inverted, and magnified.

Slide 29:

  • On the other hand, when an extended object is placed in front of a convex mirror, the image formed is always virtual, erect, and diminished.
  • The image is located between the focus and the pole of the convex mirror.
  • The size of the image decreases as the object distance increases, and it is always smaller than the object.
  • Understanding the formation of images by extended objects in spherical mirrors helps us analyze the behavior of light rays and predict how objects will appear when reflected.

Slide 30:

  • The magnification of an image formed by a spherical mirror can be calculated using the formula: m = -v/u = h’/h, where m is the magnification, v is the image distance, u is the object distance, h’ is the height of the image, and h is the height of the object.
  • The magnification can be positive for an erect image and negative for an inverted image.
  • The mirror formula, 1/v + 1/u = 1/f, relates the object distance, image distance, and focal length of a spherical mirror.
  • The sign convention for the mirror formula determines the positive and negative values of the distances.
  • Understanding the magnification and the mirror formula helps us calculate and analyze the properties of images formed by spherical mirrors.