Question

A concave mirror is used for images formation for different positions of an object. what inferences can be drawn about the following when an object is placed at a distance of 10cm from the pole of a concave mirror of focal length 15cm.
1) position of the image
2)size of the image
3) nature of the image
​

Answer 1

Given

• Focal length = -15 cm
• Mirror used = Concave
• Object Distance = -10 cm

To Find

• Image Distance
• Size and the nature of the image

Solution

● Mirror Formula :- 1/v + 1/u = 1/f

● Size of the image :- M = hᵢ/hₒ= -v/u

✭ Image Distance :

→ 1/v + 1/u = 1/f

→ 1/v + 1/-10 = 1/-15

→ 1/v - 1/10 = - 1/15

→ 1/v = 1/10 - 1/15

→ 1/v = 3/30 - 2/30

→ 1/v = (3-2)/30

→ 1/v = 1/30

→ v = 30 cm

✭ Image Size :

→ -v/u = hᵢ/hₒ

→ -30/-10 = hᵢ/hₒ

→ hᵢ = 3 cm

∴ Thr image is virtual, erect, placed at 30 cm, magnified 3 times with the image size 3 cm

Answer 2

Given:-

•A concave mirror is used for images formation for different positions of an object..

•A object is placed at a distance of 10 cm from the pole of a concave mirror of focal length 15 cm..

To Prove:-

•Position of the image

•Size of the image

•Nature of the image

Solution:-

•Focal length = - 15 cm

•Object Distance = - 10 cm

•To Find Image distance,

•Using formula,

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \red{ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} }}}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{1}{v} = \frac{1}{10} - \frac{1}{15} }}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{1}{v} = \frac{3}{30} - \frac{2}{30} }}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{1}{v} = \frac{1}{30} }}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \red{ v = 30 \: cm}}}}}}$

•To Find Size of image,

•h1 = height of the image

•h2 = height of the object

•Using Formula,

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \red{ \frac{ - v}{u} = \frac{h_</p><p>1}{h_2}}}}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \frac{ - 30}{10} = \frac{h_</p><p>1}{h_2}}}}}}$

$\leadsto{ \boxed{ \boxed{ \boxed{ \bold{ \red{h_1 = 3 \: cm }}}}}}$

•The image is virtual and erect

•The image distance is 30 cm

•The size of the image is 3 cm