An object with a height of 4.31 cm is placed 12.6 cm from a concave mirror. Determine the radius of the mirror if the image appears 8.77 cm from the mirror. Also determine the image height. 4. Repeat question 6 but for a convex mirror.

Respuesta :

Explanation:

Given that,

Height of object = 4.31 cm

Distance of the object = -12.6 cm

Distance of the image = -8.77 cm

For concave mirror,

Using mirror's formula

[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}[/tex]

[tex]\dfrac{1}{f}=\dfrac{1}{-12.6}-\dfrac{1}{8.77}[/tex]

[tex]\dfrac{1}{f}=-\dfrac{10685}{55251}[/tex]

[tex]f=-\dfrac{55251}{10685}[/tex]

[tex]f = -5.17\ cm[/tex]

Radius of the mirror is

[tex]f = |\dfrac{R}{2}|[/tex]

[tex]r=2f[/tex]

[tex]r=2\times5.17[/tex]

[tex]r=10.34\ cm[/tex]

The magnification of the mirror,

[tex]m=-\dfrac{v}{u}[/tex]

[tex]\dfrac{h_{i}}{h_{o}}=\dfrac{v}{u}[/tex]

[tex]h_{i}=-h_{o}\times\dfrac{v}{u}[/tex]

[tex]h_{i}=-4.31\times\dfrac{8.77}{12.6}[/tex]

[tex]h_{i}=-2.99\ cm[/tex]

Now, For convex mirror,

Using mirror's formula

[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}[/tex]

[tex]\dfrac{1}{f}=\dfrac{1}{-12.6}+\dfrac{1}{8.77}[/tex]

[tex]\dfrac{1}{f}=\dfrac{1915}{55251}[/tex]

[tex]f=\dfrac{55251}{1915}[/tex]

[tex]f = 28.85\ cm[/tex]

Radius of the mirror is

[tex]f = \dfrac{R}{2}[/tex]

[tex]r=2f[/tex]

[tex]r=2\times28.85[/tex]

[tex]r=57.7\ cm[/tex]

The magnification of the mirror,

[tex]m=-\dfrac{v}{u}[/tex]

[tex]\dfrac{h_{i}}{h_{o}}=\dfrac{v}{u}[/tex]

[tex]h_{i}=-h_{o}\times\dfrac{v}{u}[/tex]

[tex]h_{i}=4.31\times\dfrac{8.77}{12.6}[/tex]

[tex]h_{i}=2.99\ cm[/tex]

Hence, This is the required solution.