Slide 2: Refraction of Light

• Refraction occurs due to the change in speed of light when it passes from one medium to another
• The speed of light is different in different materials, which causes the bending of light
• Refraction can be described using Snell’s law: n1sinθ1 = n2sinθ2, where n1 and n2 are the indices of refraction of the two media, and θ1 and θ2 are the angles of incidence and refraction respectively

Slide 3: Spherical Surfaces

• Spherical surfaces are curved surfaces that can be sections of a sphere
• The center of curvature is the center of the sphere from which the spherical surface is taken
• The radius of curvature is the distance from the center of curvature to the surface

Slide 4: Object and Image Formation

• When an object is placed in front of a spherical surface, it creates an image on the other side of the surface
• The object distance (u) is the distance between the object and the spherical surface
• The image distance (v) is the distance between the image and the spherical surface

Slide 5: Sign Convention

• While dealing with refraction at spherical surfaces, we use a sign convention to determine the directions of u, v, and f (focal length)
• Distance u is positive when the object is on the incident light side, and negative when the object is on the refracted light side
• Distance v is positive when the image is on the refracted light side, and negative when the image is on the incident light side

Slide 6: Convex Spherical Surface

• A convex spherical surface is curved outward, like the outer surface of a sphere
• Convex lenses have convex spherical surfaces, and they converge light
• The radius of curvature for a convex surface is positive

Slide 7: Concave Spherical Surface

• A concave spherical surface is curved inward, like the inside surface of a sphere
• Concave lenses have concave spherical surfaces, and they diverge light
• The radius of curvature for a concave surface is negative

Slide 8: Relation between u, v, and f

• The relation between the object distance (u), image distance (v), and focal length (f) for a spherical surface is given by the lens formula: 1/f = 1/v - 1/u
• The formula relates the distances and helps us calculate the position of the image formed by a spherical surface

Slide 9: Ray Diagrams

• Ray diagrams are helpful tools to understand and visualize the formation of images by spherical surfaces
• They involve drawing incident rays from the top and bottom of the object, and refracting them through the spherical surface
• The intersection of the refracted rays reveals the position and nature (real or virtual) of the image

Slide 10: Magnification

• Magnification is a measurement of how much larger or smaller an image is compared to the object
• It can be calculated using the formula: magnification (m) = height of image (h’) / height of object (h)
• Magnification can be positive, negative, or zero, indicating whether the image is upright, inverted, or of the same size as the object, respectively

Slide 11: Refraction at Convex Spherical Surfaces

• A convex spherical surface has a positive radius of curvature (R)
• When light passes through a convex spherical surface, it converges
• The image formed by a convex spherical surface can be real or virtual, depending on the object distance Examples:
• A convex lens, like a magnifying glass or a camera lens, uses the principles of refraction at convex spherical surfaces

Slide 12: Real Image Formation - Convex Spherical Surface

• When the object is placed beyond the center of curvature (C) of a convex spherical surface, a real image is formed
• The real image is inverted and formed on the opposite side of the object
• The image distance (v) is positive for real images

Slide 13: Virtual Image Formation - Convex Spherical Surface

• When the object is placed between the center of curvature (C) and the focal point (F) of a convex spherical surface, a virtual image is formed
• The virtual image is upright and formed on the same side as the object
• The image distance (v) is negative for virtual images

Slide 14: Ray Diagram for a Convex Spherical Surface (Real Image)

• Draw an incident ray parallel to the principal axis, which passes through the focal point after refraction
• Draw an incident ray passing through the center of curvature, which continues in the same direction after refraction
• The intersection of the refracted rays gives the position of the real image Equation for convex spherical surfaces:

1/f = (n2 - n1) * (1/R)

Slide 15: Ray Diagram for a Convex Spherical Surface (Virtual Image)

• Draw an incident ray parallel to the principal axis, which appears to originate from the focal point after refraction
• Draw an incident ray passing through the center of curvature, which continues in the same direction after refraction
• The extension of the refracted rays gives the position of the virtual image

Slide 16: Refraction at Concave Spherical Surfaces

• A concave spherical surface has a negative radius of curvature (R)
• When light passes through a concave spherical surface, it diverges
• The image formed by a concave spherical surface is always virtual and upright Examples:
• A concave lens, like a diverging lens used in glasses for nearsightedness, utilize the principles of refraction at concave spherical surfaces

Slide 17: Image Formation - Concave Spherical Surface

• When light rays from an object pass through a concave spherical surface, they diverge
• The apparent intersection of the diverging rays produces a virtual image on the same side as the object
• The image formed is always virtual and upright

Slide 18: Ray Diagram for a Concave Spherical Surface

• Draw an incident ray parallel to the principal axis, which appears to originate from the focal point after refraction
• Draw an incident ray passing through the center of curvature, which continues in the same direction after refraction
• The extension of the diverging rays gives the position of the virtual image

Slide 19: Refraction at Spherical Surfaces Summary

• Refraction at spherical surfaces occurs when light passes from one medium to another through a curved surface
• Convex spherical surfaces converge light and can form real or virtual images depending on object distance
• Concave spherical surfaces diverge light and always form virtual images Equations:
• For convex spherical surfaces: 1/f = (n2 - n1) * (1/R)
• For concave spherical surfaces: No equation needed, as the image is always virtual

Slide 20: Summary and Key Points

• Refraction at spherical surfaces involves the bending of light due to the change in speed when it passes from one medium to another
• Convex spherical surfaces converge light and form real or virtual images, depending on object distance
• Concave spherical surfaces diverge light and always form virtual images
• Ray diagrams are useful tools to understand and visualize the formation of images by spherical surfaces
• Magnification is a measure of the size difference between the object and the image End of lecture.

Slide 21: Refraction at Spherical Surfaces: Examples and Applications

• Cameras and telescopes use lenses with spherical surfaces to focus light and form images
• Eyeglasses and contact lenses correct vision problems by manipulating the refraction of light using spherical surfaces
• Microscopes use lenses with spherical surfaces to magnify small objects
• Projectors and magnifying glasses also rely on refraction at spherical surfaces

Slide 22: Refraction and Power of a Lens

• The power of a lens is a measure of its ability to converge or diverge light
• The power (P) of a lens is given by the formula: P = 1/f, where f is the focal length of the lens
• Power is measured in diopters (D), where 1 D = 1/f (in meters)

Slide 23: Refraction and Lens Power: Convex Lenses

• Convex lenses have positive power because they converge light
• The power of a convex lens can be determined using the formula: P = (n - 1) * (1/R), where n is the refractive index and R is the radius of curvature

Slide 24: Refraction and Lens Power: Concave Lenses

• Concave lenses have negative power because they diverge light
• The power of a concave lens can be determined using the formula: P = (1 - n) * (1/R), where n is the refractive index and R is the radius of curvature

Slide 25: Lens Combinations

• Multiple lenses can be combined to achieve desired optical effects
• When lenses are placed close together, their powers are additive
• A lens combination can be used to focus light, correct vision, or achieve other optical goals

Slide 26: Lens Combinations: Thin Lens Formula

• The thin lens formula is used to calculate the effective focal length (f) of a combination of lenses
• The formula is given by: 1/f = 1/f1 + 1/f2 + 1/f3 + …, where f1, f2, f3, … are the focal lengths of the individual lenses

Slide 27: Lens Aberrations

• Aberrations are distortions or imperfections in the formation of images by lenses
• Spherical aberration occurs when rays passing through the edge of a lens focus at a different point compared to rays passing through the center
• Chromatic aberration occurs when different colors of light refract differently and do not focus at the same point

Slide 28: Lens Aberrations: Correction

• Spherical aberration can be reduced by using aspheric lenses, which have non-uniform curvature
• Chromatic aberration can be minimized by using achromatic lenses, which are made of multiple materials with different dispersive properties

Slide 29: Lens Aberrations: Application

• The correction of aberrations in lenses is crucial for producing high-quality images in photography, microscopy, and other fields
• Contact lenses and eyeglasses are designed to minimize aberrations and provide clear vision

Slide 30: Conclusion

• Refraction at spherical surfaces is a fundamental concept in optics
• Understanding the principles of refraction and the behavior of light at curved surfaces helps explain the formation of images by lenses
• The ability to manipulate refraction at spherical surfaces has applications in various fields, including photography, medicine, and telecommunications End of lecture.