Hey, use;
u= -24cm
f= -18cm
then,
1/f =1/u+1/v
then you use,
ho/hi=v/u.

Given:
- Distance of object from the lens (u) = 24 cm
- Focal length of the lens (f) = 18 cm

To find:
- Distance of the image from the lens (v)
- Height of the image if the object is 30 cm tall

Solution:

Step 1: Identify the type of lens
The given lens is a convex lens since the focal length (f) is positive.

Step 2: Apply the lens formula
The lens formula is given by:

1/f = 1/v - 1/u

Where:
- f is the focal length of the lens
- v is the distance of the image from the lens
- u is the distance of the object from the lens

Substituting the given values into the lens formula:

1/18 = 1/v - 1/24

Step 3: Solve the equation
To solve the equation, we can take the LCM (Least Common Multiple) of 18 and 24, which is 72. Multiplying through by 72, we get:

72/18 = 72/v - 72/24

4 = 72/v - 3

Add 3 to both sides of the equation:

7 = 72/v

Cross-multiply:

7v = 72

Divide both sides by 7:

v = 72/7

Therefore, the distance of the image from the lens is approximately 10.29 cm.

Step 4: Calculate the height of the image
The magnification formula is given by:

magnification (m) = height of image (h') / height of object (h)

The magnification is equal to the ratio of the image height to the object height. Rearranging the formula, we have:

h' = m * h

Where:
- h' is the height of the image
- h is the height of the object

Given that the object height (h) is 30 cm, we need to calculate the magnification.

Using the magnification formula:

m = -v/u

Substituting the values:

m = -10.29/24

m ≈ -0.4292

Since the magnification is negative, the image is inverted.

Now, substituting the values into the height of the image formula:

h' = -0.4292 * 30

h' ≈ -12.88 cm

Therefore, the height of the image is approximately 12.88 cm.

Conclusion:
- The distance of the image from the lens is approximately 10.29 cm.
- The height of the image is approximately 12.88 cm.