Question

An object of height 6 cm is placed at a distance of 24 cm from a concave mirror of focal length 30 cm find position height and nature of image

Answer 1

Answer:

Focal length(f) = 10 cm.

Object distance(u) = 15 cm.

Height of the Object = 6 cm.

Using the Mirror's formula,

1/f = 1/v + 1/u

⇒ 1/-10 = 1/v + 1/-15

⇒ 1/v = 1/-10 + 1/15

∴ 1/v = (-3 + 2)/30

⇒ v = -30 cm.

Since, image distance is negative, therefore, it is real and inverted.

Now, magnification = -v/u

= -(-30)/15

= 2

Since, magnification in greater than 1, therefore Image is magnified.

Also, m = H of image/H of object.

⇒ 2 = H of image/6

∴ Height of image = 12 cm.

Characteristics of Image are ⇒

Real, Inverted and Magnified.

Explanation:

Answer 2

Answer:

The image's position, height, and nature are 120cm, 30cm, and virtual, respectively.

Explanation:

From the mirror formula we have,

$\frac{1}{f}= \frac{1}{v}+ \frac{1}{u}$   (1)

Where,

f=focal length of the mirror

v=image distance from the mirror

u=object distance from the mirror

From the question we have,

Height of the object(h₁)=6cm

Object distance from the mirror(u)=-24cm

The focal length of the concave mirror(f)=-30cm

By placing the required values in equation (1) we get;

$\frac{1}{-30}= \frac{1}{v}+ \frac{1}{-24}$

$\frac{1}{-30}= \frac{1}{v}- \frac{1}{24}$

$\frac{1}{v}= \frac{1}{-30}+ \frac{1}{24}$

$\frac{1}{v}= \frac{-24+30}{30\times 24}$

$\frac{1}{v}= \frac{6}{30\times 24}$

$v=\frac{30\times 24}{6}$

$v=120cm$       (2)

The magnification of the mirror is calculated as,

$m=\frac{-v}{u}$     (3)

By putting the values of "v" and "u" in equation (3) we get;

$m=\frac{-120}{-24}$

$m=5$     (4)

Also, the magnification in terms of height is given as,

$m=\frac{h_2}{h_1}$    (5)

h₂=height of the image

h₁=height of the object

By equating equations (4) and (5) we get;

$5=\frac{h_2}{h_1}$          (6)

By placing the value of "h₁" in equation (6) we get;

$5=\frac{h_2}{6}$

$h_2=30cm$     (7)

Hence, the position, height, and nature of the image are 120cm, 30cm, and virtual respectively.

#SPJ2