Spherical Mirrors – Learning Outcomes Recognise and use key words relating to mirrors. Centre of curvature Focus / focal point, focal length Pole Principal axis Use ray tracing to demonstrate reflection. Find images in spherical mirrors using ray tracing. Describe the images formed in spherical mirrors. Differentiate between real and virtual images.

Spherical Mirrors – Learning Outcomes Use formulas to solve problems about spherical mirrors: 1 𝑓 = 1 𝑢 + 1 𝑣 𝑚= 𝑣 𝑢 Give uses of concave and convex mirrors. Measure the focal length of a concave mirror.

Spherical Mirrors

Spherical Mirrors – Ray Tracing A ray striking the pole is reflected at an equal angle with the principal axis.

Spherical Mirrors – Ray Tracing A ray passing through the centre of curvature will be reflected back through the centre of curvature.

Spherical Mirrors – Ray Tracing A ray incident parallel to the principal axis will reflect back through the focus

Spherical Mirrors – Ray Tracing A ray passing through the focus will reflect parallel to the principal axis.

Spherical Mirrors - Images Unlike in a plane mirror, spherical mirrors can form both real and virtual images. Real images are formed by the actual intersection of rays They can be formed on a screen or found by using no parallax Virtual images are formed by the apparent intersection of rays. They cannot be formed on a screen, but may be found using no parallax.

Spherical Mirrors - Images To focus an image of a distant object. Use a bright distant object (e.g. a window in a dark room). Face a concave mirror towards the object. Hold a piece of paper or cardboard in front of the mirror, and move it back and forth to focus the image. If the object was very far away, the image will form at the focus of the mirror.

Concave Mirrors - Images An object outside the centre of curvature. Image is: real inverted diminished between C and f

Concave Mirrors - Images An object at the centre of curvature. Image is: real inverted same size at C

Concave Mirrors - Images An object between the centre of curvature and the focus. Image is: real inverted magnified outside C

Concave Mirrors - Images An object at the focus. Image is: nonexistant at infinity

Concave Mirrors - Images An object inside the focus. Image is: virtual upright magnified behind mirror

Convex Mirrors – Ray Tracing A ray which strikes the pole is reflected at an equal angle to the principal axis.

Convex Mirrors – Ray Tracing A ray heading for the centre of curvature will be reflected back along its path.

Convex Mirrors – Ray Tracing A ray incident parallel to the principal axis is reflected back as if it came from the focus.

Convex Mirrors – Ray Tracing A ray travelling towards the focus is reflected parallel to the principal axis.

Convex Mirrors - Images An object anywhere in front of a convex mirror will yield the same result – image is virtual, diminished, upright, and behind the mirror.

Formula for Spherical Mirrors 1 𝑓 = 1 𝑢 + 1 𝑣 f = focal length, u = object distance, v = image distance Note that v is positive for real images, negative for virtual images. (RIP – real is positive) 𝑚= 𝑣 𝑢 m = magnification, u = object distance/height, v = image distance/height

Calculations e.g. Paulina holds a concave mirror 30cm in front of a bulb. How far from the mirror does the image form if the focal length of the mirror is 20cm? 40cm? e.g. An object is placed 30cm in front of a concave mirror. A real image of the object is formed 50cm from the mirror. What is the focal length of the mirror? If the object is 5cm high, what is the height of the image? e.g. An image is formed in a concave mirror of focal length 20cm. The image is three times the size of the object. Where must the object be placed if the image is real? What if the image is virtual?

Uses of Mirrors Concave – magnify when object inside C Dentist mirrors Cosmetic mirrors Searchlights / floodlights / car headlights Convex – wide field of view Door mirror in a car At concealed entrances At ATMs and in banks