Spherical Mirrors – Learning Outcomes Differentiate between real and virtual images. 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. Measure the focal length of a concave mirror. Find images in spherical mirrors using ray tracing. Describe the images formed in spherical mirrors.

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.

Differentiate Real and Virtual 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.

Use Key Words If the mirror were a sphere (or circle in 2D), the centre of curvature would be the centre of the sphere. The principal axis is the line joining the centre of curvature to the middle of the mirror. The pole is where the principal axis meets the mirror. In a concave mirror, the inside of the mirror is reflective.

Use Key Words The focus (aka focal point) is on the principal axis, halfway between the centre of curvature and the pole. The focal length is the distance between the focus and the pole. It is usually measured in centimetres. In a convex mirror, the outside of the mirror is reflective.

Use Ray Tracing – Concave Mirror A ray striking the pole is reflected at an equal angle with the principal axis.

Use Ray Tracing – Concave Mirror A ray passing through the centre of curvature will be reflected back through the centre of curvature.

Use Ray Tracing – Concave Mirror A ray incident parallel to the principal axis will reflect back through the focus.

Use Ray Tracing – Concave Mirror A ray passing through the focus will reflect parallel to the principal axis.

Use Ray Tracing – Concave Mirror Concave mirror simulation An object outside the centre of curvature. Image is: real inverted diminished between C and f

Use Ray Tracing – Concave Mirror Concave mirror simulation An object at the centre of curvature. Image is: real inverted same size at C

Use Ray Tracing – Concave Mirror Concave mirror simulation An object between the centre of curvature and the focus. Image is: real inverted magnified outside C

Use Ray Tracing – Concave Mirror Concave mirror simulation An object at the focus. Image is: nonexistant at infinity

Use Ray Tracing – Concave Mirror Concave mirror simulation An object inside the focus. Image is: virtual upright magnified behind mirror

Measure the Focal Length 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.

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

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

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

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

Use Ray Tracing – Convex Mirror Convex mirror simulation An object anywhere in front of a convex mirror will yield the same result – image is virtual, diminished, upright, and behind the mirror.

Solve Problems about Spherical Mirrors Formula: 1 𝑓 = 1 𝑢 + 1 𝑣 𝑓 = focal length, 𝑢 = object distance, 𝑣 = image distance Note that image distance is positive for real images (in front of the mirror), negative for virtual images (behind the mirror): RIP – real is positive. Similarly, focal length is positive for concave mirrors and negative for convex mirrors. Formula: 𝑚= 𝑣 𝑢 𝑚 = magnification, 𝑢 = object distance/height, 𝑣 = image distance/height magnification can be positive or negative, giving some questions two answers

Solve Problems about Spherical Mirrors e.g. Paulina holds a concave mirror 30 cm in front of a bulb. How far from the mirror does the image form if the focal length of the mirror is 20 cm? What if the focal length is 40 cm? e.g. Dagmara looks into the back of a spoon (effectively a convex mirror). When her eye is 10 cm from the spoon, she sees the image of her eye 5.5 cm behind the spoon. What is the focal length of the spoon? 1 𝑓 = 1 𝑢 + 1 𝑣 𝑚= 𝑣 𝑢

Solve Problems about Spherical Mirrors 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? 1 𝑓 = 1 𝑢 + 1 𝑣 𝑚= 𝑣 𝑢

Solve Problems about Spherical Mirrors e.g. When an object is placed in front of a concave mirror of focal length 15cm, the image is three times the size of the object. Where is the object placed if the image is real? Where is the object placed if the image is virtual? 1 𝑓 = 1 𝑢 + 1 𝑣 𝑚= 𝑣 𝑢

Give 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