What is reflection? Spherical mirrors can be either convex or concave - Leaving Cert Physics - Question b - 2014

To draw a ray diagram for a convex mirror:

1. Start by drawing the convex mirror as a curved line.
2. Indicate the focal point (F), located behind the mirror at a distance of 5 cm from the mirror.
3. Draw an object (such as an arrow) placed in front of the mirror.
4. From the top of the object, draw one ray parallel to the principal axis that reflects off the mirror and diverges outward, as if it comes from the focal point.
5. Draw a second ray that hits the vertex of the mirror and reflects back at an angle equal to the angle of incidence.
6. Extend the reflected rays backward to locate the virtual image where they appear to converge.

To find the position of the image:

1. Determine the focal length (f) of the convex mirror:
   f = r/2 = 20 cm / 2 = 10 cm, thus f = 5 cm.
2. The object distance (u) is given as 30 cm (positive for virtual object in convex mirrors).
3. Apply the mirror formula:
   $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
   $\frac{1}{5} = \frac{1}{30} + \frac{1}{v}$
4. Rearranging gives:
   $\frac{1}{v} = \frac{1}{5} - \frac{1}{30} = \frac{6-1}{30} = \frac{5}{30}$
5. Therefore, v = 30/5 = 6 cm. Since the image is virtual, it is located behind the mirror at a distance of 4.3 cm.

Dentists prefer concave mirrors because they can provide a magnified and upright image of the teeth. This allows for better visibility and examination of dental structures. In contrast, convex mirrors produce diminished images, which are less effective for detailed inspections.