Babies and their fears
Babies of a year may become fascinated with one thing for several weeks on - for instance, the telephone, planes over head, electric lights (in my case, the wash machine). We should let them touch and become familiar with objects that are not dangerous or disturbing. It's also wiser for us, parents, not to play up to their interest, or, if it's something dangerous,not to dwell on the danger. It's better to distract them with something else, then to increase their awe.
At this age babies may be frightened by strange objects that move suddenly or make a loud noise, such as folded pictures that popup from a book, the opening of an umbrella, a vacuum cleaner, a siren, a barking jumping dog, a train, etc.
Try not to have these startling things too close to 1-year-olds until they get used to them. If the vacuum cleaner bothers them, try not to use it for a while, at least while they're nearby. Then try it the first time when they are some distance away.

Fear of the bath
Between 1 and 2 years, a child may become frightened of the bath, because of slipping under water, or getting soap in the eyes, or even seeing and hearing the water go down the drain (my little girl has 3 years old and she's still frightened of the bath). To avoid soap in the eyes, soap with a washcloth that is not too wet and rinse several times with a damp but not dripping washcloth. There are also special shampoos for children that sting less.
Fear of the darkness

Sometimes babies just need to be held in your arms, and just like us, when we fear to stay in the darkness, or walk alone at night, for example, he needs to avoid such things and be distracted by others. It's difficult to postpone the bath time, but we simply should make them forget for one day or two about it, and think about a better method for our child's bathing in the meantime. My daughter hates water in her eyes or ears, but now, we've found a method when washing her hair: she puts on her sunglasses, and fingers in her ears when cleaning her shampooned hair. This is our method, and it worked for the moment.
Babies who have fears shouldn't be forced at all to do anything and should be raised in a positive manner.
Text source: Dr. Spock's Baby and Child Care -Beanjamin Spock and Michael Rothenberg