Answer to Question #286520 in Physics for allen

Question

determine the image distance and image height for a 5.00 cm tall object placed 10.0 cm from a concave mirror having a focal length of 15.0 cm

Answer 1

Apply thin lens equation:

$$\dfrac 1f=\dfrac 1o+\dfrac1i,\\\space\\ i=\dfrac{of}{o-f}=\dfrac{(-10)(-15)}{(-10)-(-15)}=30\text{ cm}.$$

From magnification, find the image height:

$$M=-\dfrac io=\dfrac{h_i}{h_o}→h_i=-\dfrac{h_oi}{o}=-\dfrac{5·30}{-10}=15\text{ cm}.$$