A concave mirror of focal length 10 cm forms an upright and diminished image of a real object placed at a distance of 5 cm from the mirror. Is this true or false?

Respuesta :

Given,

The focal length of the concave mirror, f=10 cm

The object distance, o=5 cm

From the mirror formula, we have,

[tex]\frac{1}{f}=\frac{1}{o}+\frac{1}{i}[/tex]

Where i is the image distance.

On substituting the known formula,

[tex]\begin{gathered} \frac{1}{10}=\frac{1}{5}+\frac{1}{i} \\ \Rightarrow\frac{1}{i}=\frac{1}{10}-\frac{1}{5} \\ =-\frac{1}{10} \\ \Rightarrow i=-10\text{ cm} \end{gathered}[/tex]

And the magnification is given by,

[tex]m=\frac{-i}{o}[/tex]

On substituting the known values,

[tex]\begin{gathered} m=\frac{-(-10)}{5} \\ =2 \end{gathered}[/tex]

Thus the object is not diminished, it is magnified.

Thus the given statement is false.