Spherical mirrors are mirrors with a spherical reflecting surface. These mirrors are part of a sphere and can be either concave (curved inward) or convex (curved outward). They follow the basic principles of reflection and are used in a wide range of applications such as telescopes, microscopes, and vehicle mirrors.
Definition of Spherical Mirrors
A spherical mirror is a mirror whose surface is a portion of a sphere. The spherical surface may be a concave mirror (curved inward) or a convex mirror (curved outward).
- Concave Mirror: Reflecting surface is curved inward (like the inside of a sphere).
- Convex Mirror: Reflecting surface is curved outward (like the outside of a sphere).
Types of Spherical Mirrors
- Concave Mirror 🪞🔍
- Shape: Curved inward, like the inside of a sphere.
- Reflection: Parallel rays of light converge to a single focal point after reflecting off the mirror.
- Applications: Used in applications like shaving mirrors, satellite dishes, telescopes, and headlights.
- Convex Mirror 🪞👀
- Shape: Curved outward, like the outside of a sphere.
- Reflection: Parallel rays of light diverge after reflecting off the mirror, making them appear to come from a focal point behind the mirror.
- Applications: Used in vehicle side mirrors, security mirrors, and as rearview mirrors because they provide a wide field of view.
Formation of Images in Spherical Mirrors
The formation of images in spherical mirrors depends on the position of the object relative to the mirror. The image can be real or virtual, and its size can be magnified or diminished based on the object’s distance from the mirror.
- Concave Mirror:
- Real Image: Formed when the object is outside the focal point (object distance is greater than the focal length). The image is inverted and can be projected onto a screen.
- Virtual Image: Formed when the object is inside the focal point (object distance is less than the focal length). The image is upright and cannot be projected.
- Convex Mirror:
- Always Forms a Virtual Image: The image is always upright, diminished, and appears to be located behind the mirror, regardless of the object’s position.
Mirror Formula
The mirror formula relates the focal length (f), object distance (u), and image distance (v) for any spherical mirror. It is given by:
Where:
- f = Focal length of the mirror
- v = Image distance (distance from the mirror to the image)
- u = Object distance (distance from the mirror to the object)
This formula is valid for both concave and convex mirrors, with the sign conventions depending on the type of mirror:
- For a concave mirror:
- Focal length (f) is positive.
- Image distance (v) is positive for real images and negative for virtual images.
- For a convex mirror:
- Focal length (f) is negative.
- Image distance (v) is always negative.
Sign Conventions for Spherical Mirrors
- Object Distance (u): Measured from the mirror along the principal axis.
- Negative if the object is in front of the mirror (real object).
- Positive if the object is behind the mirror (virtual object).
- Image Distance (v): Distance from the mirror to the image formed.
- Negative if the image is formed behind the mirror (virtual image).
- Positive if the image is formed in front of the mirror (real image).
- Focal Length (f):
- Positive for concave mirrors.
- Negative for convex mirrors.
Magnification Formula
The magnification (M) produced by a spherical mirror is given by:
Where:
- h’ = Height of the image
- h = Height of the object
- v = Image distance
- u = Object distance
The magnification tells you how much larger or smaller the image is compared to the object. If M > 1, the image is magnified, and if M < 1, the image is reduced in size.
Summary of Key Points
- Types: Concave mirrors (converging) and convex mirrors (diverging).
- Mirror Formula: 1f=1/v+1/u
- Magnification: M = v/u
- Applications: Concave mirrors focus light, while convex mirrors spread light.