Optics- Reflection of Light and Formation of Images

Reflection of ray incident at pole:

• When a ray of light is incident on a concave mirror, passing through its pole, it reflects back along the same path.
• The angle of incidence is equal to the angle of reflection.
• The incident ray, the reflected ray, and the normal to the mirror, all lie in the same plane.

Formation of Images:

• Images formed by concave mirrors can be real or virtual, depending on the position of the object.
• When the object is beyond the focus of the mirror, a real, inverted, and diminished image is formed.
• When the object is at the focus of the mirror, no image is formed.
• When the object is between the focus and the pole of the mirror, a virtual, erect, and magnified image is formed.

Laws of Reflection:

• The incident ray, the reflected ray, and the normal to the mirror, all lie in the same plane.
• The angle of incidence is equal to the angle of reflection.

Image Characteristics:

• The image formed by a concave mirror can be real or virtual.
• Real images can be projected on a screen and are formed when the object is beyond the focus.
• Virtual images cannot be projected on a screen and are formed when the object is between the focus and the pole.

Sign Convention:

• In the case of reflection in a concave mirror, the object is always placed on the left side of the mirror.
• Distances measured in the same direction as the incident light are positive, while distances measured in the opposite direction are negative.

11. Reflection of ray incident at pole:

• Concave mirrors are curved inwards and have a reflective surface on the inner side.
• When a ray of light is incident on a concave mirror, passing through its pole, it reflects back along the same path.
• This is due to the curvature of the mirror, which causes the reflected rays to converge.

12. Angle of incidence and angle of reflection:

• According to the laws of reflection, the angle of incidence is equal to the angle of reflection.
• The incident ray, the reflected ray, and the normal to the mirror all lie in the same plane.
• This can be observed when a beam of light is incident on a concave mirror and reflects back.

13. Formation of Images by concave mirrors:

• When an object is placed beyond the focus of a concave mirror, a real, inverted, and diminished image is formed.
• This image can be projected on a screen and is formed due to the convergence of the reflected rays.
• Examples of such images can be seen in optical devices like telescopes and binoculars.

14. No image formation at the focus:

• When an object is placed at the focus of a concave mirror, no image is formed.
• This is because the reflected rays become parallel and do not converge to form an image.
• This condition can be used to create a parallel beam of light in various optical systems.

15. Image formation between the focus and the pole:

• When an object is placed between the focus and the pole of a concave mirror, a virtual, erect, and magnified image is formed.
• This image is formed due to the divergence of the reflected rays.
• Examples of such images can be seen in makeup mirrors and shaving mirrors.

16. Relation between object distance (u), image distance (v), and focal length (f):

• In the case of concave mirrors, the relation between the object distance, image distance, and focal length can be given by the mirror formula: 1/f = 1/v + 1/u.
• Here, f represents the focal length, v represents the image distance, and u represents the object distance.
• This formula can be used to calculate the position and characteristics of the image formed by a concave mirror.

17. Magnification of the image:

• The magnification (m) of the image formed by a concave mirror can be defined as the ratio of the height of the image to the height of the object.
• It can be calculated using the formula: m = -v/u, where v is the image distance and u is the object distance.
• The magnification can be positive or negative, depending on whether the image is erect or inverted.

18. Real and virtual images:

• Real images are formed when the object is placed beyond the focal point of a concave mirror.
• These images can be projected on a screen and are always inverted.
• Virtual images, on the other hand, are formed when the object is placed within the focal length of the mirror.
• These images cannot be projected on a screen and are always erect.

19. Sign convention for concave mirrors:

• In the case of reflection in a concave mirror, distances measured in the same direction as the incident light are considered positive.
• Distances measured in the opposite direction are considered negative.
• The object is always placed on the left side of the mirror, as per the sign convention.
• This convention helps in consistent calculations when dealing with mirror formula and magnification equations.

20. Example problems:

• A concave mirror has a focal length of 20 cm. An object is placed at a distance of 40 cm from the mirror. Find the position and nature of the image formed.
• A concave mirror forms a real, inverted, and magnified image of an object. If the height of the object is 2 cm and the height of the image is 6 cm, calculate the magnification and the position of the image.
• These example problems illustrate the application of mirror formulas and magnification calculations in determining the characteristics of images formed by concave mirrors.

21. Reflection of ray incident at pole:

• When a ray of light is incident on a concave mirror, passing through its pole, it reflects back along the same path.
• The angle of incidence is equal to the angle of reflection.
• The incident ray, the reflected ray, and the normal to the mirror, all lie in the same plane.

22. Angle of incidence and angle of reflection:

• According to the laws of reflection, the angle of incidence is equal to the angle of reflection.
• The incident ray, the reflected ray, and the normal to the mirror all lie in the same plane.
• This can be observed when a beam of light is incident on a concave mirror and reflects back.

23. Formation of Images by concave mirrors:

• When an object is placed beyond the focus of a concave mirror, a real, inverted, and diminished image is formed.
• This image can be projected on a screen and is formed due to the convergence of the reflected rays.
• Examples of such images can be seen in optical devices like telescopes and binoculars.

24. No image formation at the focus:

• When an object is placed at the focus of a concave mirror, no image is formed.
• This is because the reflected rays become parallel and do not converge to form an image.
• This condition can be used to create a parallel beam of light in various optical systems.

25. Image formation between the focus and the pole:

• When an object is placed between the focus and the pole of a concave mirror, a virtual, erect, and magnified image is formed.
• This image is formed due to the divergence of the reflected rays.
• Examples of such images can be seen in makeup mirrors and shaving mirrors.

26. Relation between object distance (u), image distance (v), and focal length (f):

• In the case of concave mirrors, the relation between the object distance, image distance, and focal length can be given by the mirror formula: 1/f = 1/v + 1/u.
• Here, f represents the focal length, v represents the image distance, and u represents the object distance.
• This formula can be used to calculate the position and characteristics of the image formed by a concave mirror.

27. Magnification of the image:

• The magnification (m) of the image formed by a concave mirror can be defined as the ratio of the height of the image to the height of the object.
• It can be calculated using the formula: m = -v/u, where v is the image distance and u is the object distance.
• The magnification can be positive or negative, depending on whether the image is erect or inverted.

28. Real and virtual images:

• Real images are formed when the object is placed beyond the focal point of a concave mirror.
• These images can be projected on a screen and are always inverted.
• Virtual images, on the other hand, are formed when the object is placed within the focal length of the mirror.
• These images cannot be projected on a screen and are always erect.

29. Sign convention for concave mirrors:

• In the case of reflection in a concave mirror, distances measured in the same direction as the incident light are considered positive.
• Distances measured in the opposite direction are considered negative.
• The object is always placed on the left side of the mirror, as per the sign convention.
• This convention helps in consistent calculations when dealing with mirror formula and magnification equations.

30. Example problems:

• A concave mirror has a focal length of 20 cm. An object is placed at a distance of 40 cm from the mirror. Find the position and nature of the image formed.
• A concave mirror forms a real, inverted, and magnified image of an object. If the height of the object is 2 cm and the height of the image is 6 cm, calculate the magnification and the position of the image.
• These example problems illustrate the application of mirror formulas and magnification calculations in determining the characteristics of images formed by concave mirrors.