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A 3 cm tall object is 45 cm in front of a convex mirror that has a -25 cm focal length. What is the image characteristics? Real / Virtual Upright / Inverted Smaller / Larger / Same Size O A. Real Inverted Larger OB. Real Upright Smaller O C. Vitual Inverted Larger O D. Virtual Upright Smaller

Respuesta :

Explanation:

It is given that,

Height of the object, h = 3 cm

Object distance, u = -45 cm

Focal length of the mirror, f = - 25 cm

Using mirror's formula as :

[tex]\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}[/tex], v is the image distance

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

[tex]\dfrac{1}{v}=\dfrac{1}{-25}-\dfrac{1}{-45}[/tex]

v = −56.25 cm

Let h' is the height of the image. Using the formula of magnification as :

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

[tex]h'=\dfrac{-vh}{u}[/tex]

[tex]h'=\dfrac{-(-56.25)\times 3}{-45}[/tex]

[tex]h'=+3.75\ cm[/tex]

So, the image is larger than object. The image is upright and inverted. Hence, this is the required solution.